Items tagged with fsolve

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hello.i have a problem for solving this equation.i dont why my past post about this is deleted.!!!

please help me

thanks,,,

9.mw
 

restart:

A1:= 27159:  n:= 0.59:  A2:= 70941:  h0:= 3e-4:   
L:= 0.8:  dpx := -98100:  uc:= 0.007:  k:=2.7:

ODE:= (A3,y)->
   (h0^(n+1)*L/sqrt(n)*(A1*exp(sqrt(n)*y/L)-A2*exp(-sqrt(n)*y/L))/k+dpx*y*h0^(n+1)/k+A3*(h0)^n/k)^(1/n)
;

proc (A3, y) options operator, arrow; (h0^(n+1)*L*(A1*exp(sqrt(n)*y/L)-A2*exp(-sqrt(n)*y/L))/(sqrt(n)*k)+dpx*y*h0^(n+1)/k+A3*h0^n/k)^(1/n) end proc

(1)

ODEINT:= proc(A3)
option remember;
local y;
   evalf(Int(ODE(A3,y), y= 0..1, epsilon= 1e-7)) - uc
end proc:

ReINT:= proc(A3x, A3y)
   Digits:= 15:
   Re(ODEINT(A3x + I*A3y))
end proc:

ImINT:= subs(Re= Im, eval(ReINT)):

Digits:= 7:
a3:= fsolve([ReINT, ImINT]);

fsolve([ReINT, ImINT])

(2)

A3:= Complex(a3[]);

Complex(fsolve([ReINT, ImINT])[])

(3)

Solve as IVP:

Digits:= 15:
sol:= dsolve({diff(u(y),y) = ODE(A3,y), u(0)=0}, numeric, range=0..1,  output=listprocedure):

Warning,  computation interrupted

 

NULL

``

NULL

NULL

plots:-odeplot(
   sol, [[y, Re(u(y))], [y, Im(u(y))]], y= 0..1,
   legend= [real, imag], labels= [y, u(y)]
);

Verify that boundary condition at u(1) is satisfied:

 

 

 

abs(eval(u(y), sol(1)) - uc);

sol(.5);

"\"

fy3 := eval(u(y), sol); with(CurveFitting); fy33 := PolynomialInterpolation([[0, fy3(0)], [.1, fy3(.1)], [.2, fy3(.2)], [.3, fy3(.3)], [.4, fy3(.4)], [.5, fy3(.5)], [.6, fy3(.6)], [.7, fy3(.7)], [.8, fy3(.8)], [.9, fy3(.9)], [1, fy3(1)]], y)

DEBI := int(fy33, y = 0 .. 1)

NULL

``

plot(DEBI, y = 0 .. 1)

``

``

``

``

``


 

Download 9.mw

 

Greetings Sirs,

I have recently aquired Maple for some mathematics, and being a new user, I basically google for everything at the moment.

While it has gone well so far, I seem to have hit a bump that I cannot figure out.

I have a function: f(x)=3.2+0.4sin(1.25x), 0<x<5

Trying to find the places where "f(x)=3.5" would normally be done with the equation "3.5=3.2+0.4sin(1.25x)", and when I solve for the equation in Maple I get a solution too.

Problem is though, I know there is supposed to be multiple solutions. Having used wolframalpha, and being capable of seeing the plot in Maple, I know there is two points within the period "x=0..5" that is the solution.

But when I try to solve the equation, I get only one solution per solve, and the second solve doesn't make much sense for me. These are what I use:

As you can see, in the first solve the entire function is being taking into consideration, yet I only get one solution... In the second solve I have tried specifying a period, but I still only get one solution.

Basically any help here is appreciated, because from what I understand, having read google, the solve command or fsolve command is supposed to give multiple results if they are there.

With appreciation,
Ciesi

(Edit: Image size changed)

when i want to get awenser i have to solve it for 36 equation and 36 variabales
but maple will not give me a solution (just toss me back my variabales ) i dont know whats wrong
it will give me an awenser for lower like 20equ and 20var ?
parameters :

there is m for power an equation (equation^m) its between 2 , 2.5 , 3 , 4
and N give 2N+2var and 2N+2equ
its a hard calculation i copy it here hope u get it

h= "a number "

p := proc (x) c[-N-1]*x^2+1 end proc

dp := diff(p(x), x)

ddp := diff(p(x), x, x)

DELTA2 := piecewise(k <> j, -2*(-1)^(j-k)/(j-k)^2, k = j, -(1/3)*Pi^2)/h^2

DELTA1 := piecewise(k <> j, (-1)^(j-k)/(j-k), k = j, 0)/h

DELTA0 := piecewise(k <> j, 0, k = j, 1)

PHI := proc (x) ln(sinh(x)) end proc

dPHI := diff(PHI(x), x)

ddPHI := diff(PHI(x), x, x)
 

for i from -N-1 to N do x[i] := ln(exp(i*h)+(exp(2*i*h)+1)^(1/2)) end do

variabales : c[-N-1],c[-N],c[-N+1]...c[N-1],c[N] total 2N+2 var



My equations

POL := seq(simplify(eval(sum(c[k]*((eval(2*dPHI*DELTA1), x = x[j])+eval(x[j]*ddPHI*DELTA1, x = x[j])+x[j]*(eval(dPHI^2, x = x[j]))*DELTA2), k = -N .. N)+eval(ddp, x = x[j])+2*(sum(c[k]*(eval(x[j]*dPHI*DELTA1, x = x[j])+DELTA0), k = -N .. N)+eval(dp, x = x[j]))/x[j]+(c[j]*x[j]+p(x[j]))^m, x = x[j])), j = -N-1 .. N)

solving

K := fsolve({seq(POL[v] = 0, v = 1 .. 2*N+2)})

it can calculate for m=2.5 , N=15 , h=0.29669

if you can calculate it for m=3 , N=17 , h=0.41600

Regarding my recent question http://www.mapleprimes.com/questions/221909-How-To-Extract-Data-From-Implicit-Function I would like to share an interesting observation. Here the code of the program:

restart;
R0 := ln(y)+Re(Psi(1/2+(2*(p^2+(1/2)*sqrt(2*I+4*ksi_fs^2*p^2)*tanh(sqrt(2*I+4*ksi_fs^2*p^2)*x)/(tau+0.5e-2*a)))/y))+gamma+2*ln(2)
tau:= 10.000:ksi_fs:=10:p:=0.037:
R0p:= unapply(R0, [a,x]):
R0f:= proc(a,x)
local r:= fsolve(R0p(a,x), y= 0..1);
   `if`(r::float, r, Float(undefined))
end proc:
M:= Matrix(
   (100,100),
   (i,j)-> R0f(i, 1 + (j-1)*(0.5-0)/(100-1)),
   datatype= float[8]
);

After approximately 2 hours of calculations I get a message window

But I repeat this calculations on another computer with the same Windows 7 64 bit and Maple 17 I don't get such error and I obtain desired data.

So can Maple be sensitive to the hardware? 

I am trying to solve system consisting of two equations and two unknowns. I tried solve but it gives back unevaluated then I tried fsolve which gives an error.
 

restart; x := 2.891022275*`&epsilon;`^4*sin(phi)^5*cos(phi)+1.080128320*`&epsilon;`^8*sin(phi)^11*cos(phi)+.1742483217*`&epsilon;`^10*sin(phi)^9*cos(phi)+3.293959886*`&epsilon;`^4*sin(phi)^15*cos(phi)+0.1414814731e-3*`&epsilon;`^12*sin(phi)*cos(phi)+0.1186386550e-1*`&epsilon;`^10*sin(phi)^3*cos(phi)+4.689119196*`&epsilon;`^2*sin(phi)^11*cos(phi)+.2775645236*`&epsilon;`^8*sin(phi)^5*cos(phi)+2.242139502*`&epsilon;`^6*sin(phi)^7*cos(phi)+6.170463035*`&epsilon;`^4*sin(phi)^9*cos(phi)+.2212715683*`&epsilon;`^2*sin(phi)*cos(phi)+.2565381358*`&epsilon;`^4*sin(phi)*cos(phi)+6.282275004*`&epsilon;`^4*sin(phi)^11*cos(phi)+0.9582543506e-5*`&epsilon;`^14*sin(phi)*cos(phi)+1.375810863*`&epsilon;`^2*sin(phi)^3*cos(phi)+0.4588193106e-1*`&epsilon;`^10*sin(phi)^5*cos(phi)+.6194422970*`&epsilon;`^8*sin(phi)^7*cos(phi)+0.1249753779e-2*`&epsilon;`^12*sin(phi)^3*cos(phi)+3.258184644*`&epsilon;`^6*sin(phi)^9*cos(phi)+3.520102051*`&epsilon;`^2*sin(phi)^13*cos(phi)+0.9608710101e-4*`&epsilon;`^14*sin(phi)^3*cos(phi)+5.222697446*`&epsilon;`^4*sin(phi)^13*cos(phi)+0.4740690151e-6*`&epsilon;`^16*sin(phi)*cos(phi)+.1124269022*`&epsilon;`^10*sin(phi)^7*cos(phi)+0.5349926002e-2*`&epsilon;`^12*sin(phi)^5*cos(phi)+.9885168554*`&epsilon;`^8*sin(phi)^9*cos(phi)+3.656113028*`&epsilon;`^6*sin(phi)^11*cos(phi)+2.252753163*`&epsilon;`^2*sin(phi)^15*cos(phi)+0.1562649478e-2*`&epsilon;`^10*sin(phi)*cos(phi)+0.8234222560e-1*`&epsilon;`^8*sin(phi)^3*cos(phi)+0.1277730241e-1*`&epsilon;`^12*sin(phi)^7*cos(phi)+1.148250169*`&epsilon;`^6*sin(phi)^5*cos(phi)+0.4933078791e-5*`&epsilon;`^16*sin(phi)^3*cos(phi)+4.857729947*`&epsilon;`^4*sin(phi)^7*cos(phi)+5.282506255*`&epsilon;`^2*sin(phi)^9*cos(phi)+0.1560418629e-7*`&epsilon;`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.6645139802*sin(phi)^11*cos(phi)+0.4077214292e-3*`&epsilon;`^14*sin(phi)^5*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+4.820745909*`&epsilon;`^2*sin(phi)^7*cos(phi)+1.134364300*`&epsilon;`^2*sin(phi)^17*cos(phi)+0.7437311918e-1*`&epsilon;`^6*sin(phi)*cos(phi)+0.1283200926e-1*`&epsilon;`^8*sin(phi)*cos(phi)+1.168884099*`&epsilon;`^4*sin(phi)^3*cos(phi)+.3981616844*`&epsilon;`^6*sin(phi)^3*cos(phi)+3.270035435*`&epsilon;`^2*sin(phi)^5*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+2.975771526*`&epsilon;`^6*sin(phi)^13*cos(phi); y := 2.891022275*`&epsilon;`^4*sin(phi)^5*cos(phi)+1.080128320*`&epsilon;`^8*sin(phi)^11*cos(phi)+.1742483217*`&epsilon;`^10*sin(phi)^9*cos(phi)+3.293959886*`&epsilon;`^4*sin(phi)^15*cos(phi)+0.1414814731e-3*`&epsilon;`^12*sin(phi)*cos(phi)+0.1186386550e-1*`&epsilon;`^10*sin(phi)^3*cos(phi)+4.689119196*`&epsilon;`^2*sin(phi)^11*cos(phi)+.2775645236*`&epsilon;`^8*sin(phi)^5*cos(phi)+2.242139502*`&epsilon;`^6*sin(phi)^7*cos(phi)+6.170463035*`&epsilon;`^4*sin(phi)^9*cos(phi)+.2212715683*`&epsilon;`^2*sin(phi)*cos(phi)+.2565381358*`&epsilon;`^4*sin(phi)*cos(phi)+6.282275004*`&epsilon;`^4*sin(phi)^11*cos(phi)+0.9582543506e-5*`&epsilon;`^14*sin(phi)*cos(phi)+1.375810863*`&epsilon;`^2*sin(phi)^3*cos(phi)+0.4588193106e-1*`&epsilon;`^10*sin(phi)^5*cos(phi)+.6194422970*`&epsilon;`^8*sin(phi)^7*cos(phi)+0.1249753779e-2*`&epsilon;`^12*sin(phi)^3*cos(phi)+3.258184644*`&epsilon;`^6*sin(phi)^9*cos(phi)+3.520102051*`&epsilon;`^2*sin(phi)^13*cos(phi)+0.9608710101e-4*`&epsilon;`^14*sin(phi)^3*cos(phi)+5.222697446*`&epsilon;`^4*sin(phi)^13*cos(phi)+0.4740690151e-6*`&epsilon;`^16*sin(phi)*cos(phi)+.1124269022*`&epsilon;`^10*sin(phi)^7*cos(phi)+0.5349926002e-2*`&epsilon;`^12*sin(phi)^5*cos(phi)+.9885168554*`&epsilon;`^8*sin(phi)^9*cos(phi)+3.656113028*`&epsilon;`^6*sin(phi)^11*cos(phi)+2.252753163*`&epsilon;`^2*sin(phi)^15*cos(phi)+0.1562649478e-2*`&epsilon;`^10*sin(phi)*cos(phi)+0.8234222560e-1*`&epsilon;`^8*sin(phi)^3*cos(phi)+0.1277730241e-1*`&epsilon;`^12*sin(phi)^7*cos(phi)+1.148250169*`&epsilon;`^6*sin(phi)^5*cos(phi)+0.4933078791e-5*`&epsilon;`^16*sin(phi)^3*cos(phi)+4.857729947*`&epsilon;`^4*sin(phi)^7*cos(phi)+5.282506255*`&epsilon;`^2*sin(phi)^9*cos(phi)+0.1560418629e-7*`&epsilon;`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.6645139802*sin(phi)^11*cos(phi)+0.4077214292e-3*`&epsilon;`^14*sin(phi)^5*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+4.820745909*`&epsilon;`^2*sin(phi)^7*cos(phi)+1.134364300*`&epsilon;`^2*sin(phi)^17*cos(phi)+0.7437311918e-1*`&epsilon;`^6*sin(phi)*cos(phi)+0.1283200926e-1*`&epsilon;`^8*sin(phi)*cos(phi)+1.168884099*`&epsilon;`^4*sin(phi)^3*cos(phi)+.3981616844*`&epsilon;`^6*sin(phi)^3*cos(phi)+3.270035435*`&epsilon;`^2*sin(phi)^5*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+2.975771526*`&epsilon;`^6*sin(phi)^13*cos(phi); evalf(solve({x = 0, y = 0}, {phi, `&epsilon;`})); fsolve({x = 0, y = 0}, {phi, `&epsilon;`})

.9885168554*`&epsilon;`^8*sin(phi)^9*cos(phi)+0.1249753779e-2*`&epsilon;`^12*sin(phi)^3*cos(phi)+3.258184644*`&epsilon;`^6*sin(phi)^9*cos(phi)+.1124269022*`&epsilon;`^10*sin(phi)^7*cos(phi)+0.4588193106e-1*`&epsilon;`^10*sin(phi)^5*cos(phi)+.2565381358*`&epsilon;`^4*sin(phi)*cos(phi)+6.282275004*`&epsilon;`^4*sin(phi)^11*cos(phi)+0.4933078791e-5*`&epsilon;`^16*sin(phi)^3*cos(phi)+5.282506255*`&epsilon;`^2*sin(phi)^9*cos(phi)+2.242139502*`&epsilon;`^6*sin(phi)^7*cos(phi)+6.170463035*`&epsilon;`^4*sin(phi)^9*cos(phi)+0.8234222560e-1*`&epsilon;`^8*sin(phi)^3*cos(phi)+0.9608710101e-4*`&epsilon;`^14*sin(phi)^3*cos(phi)+3.656113028*`&epsilon;`^6*sin(phi)^11*cos(phi)+5.222697446*`&epsilon;`^4*sin(phi)^13*cos(phi)+0.1562649478e-2*`&epsilon;`^10*sin(phi)*cos(phi)+.6194422970*`&epsilon;`^8*sin(phi)^7*cos(phi)+3.520102051*`&epsilon;`^2*sin(phi)^13*cos(phi)+0.1186386550e-1*`&epsilon;`^10*sin(phi)^3*cos(phi)+4.689119196*`&epsilon;`^2*sin(phi)^11*cos(phi)+1.375810863*`&epsilon;`^2*sin(phi)^3*cos(phi)+0.4740690151e-6*`&epsilon;`^16*sin(phi)*cos(phi)+0.4077214292e-3*`&epsilon;`^14*sin(phi)^5*cos(phi)+0.9582543506e-5*`&epsilon;`^14*sin(phi)*cos(phi)+0.5349926002e-2*`&epsilon;`^12*sin(phi)^5*cos(phi)+.1742483217*`&epsilon;`^10*sin(phi)^9*cos(phi)+1.148250169*`&epsilon;`^6*sin(phi)^5*cos(phi)+0.1277730241e-1*`&epsilon;`^12*sin(phi)^7*cos(phi)+0.7437311918e-1*`&epsilon;`^6*sin(phi)*cos(phi)+1.080128320*`&epsilon;`^8*sin(phi)^11*cos(phi)+2.975771526*`&epsilon;`^6*sin(phi)^13*cos(phi)+1.134364300*`&epsilon;`^2*sin(phi)^17*cos(phi)+3.293959886*`&epsilon;`^4*sin(phi)^15*cos(phi)+1.168884099*`&epsilon;`^4*sin(phi)^3*cos(phi)+3.270035435*`&epsilon;`^2*sin(phi)^5*cos(phi)+0.1283200926e-1*`&epsilon;`^8*sin(phi)*cos(phi)+4.820745909*`&epsilon;`^2*sin(phi)^7*cos(phi)+.3981616844*`&epsilon;`^6*sin(phi)^3*cos(phi)+2.891022275*`&epsilon;`^4*sin(phi)^5*cos(phi)+0.1414814731e-3*`&epsilon;`^12*sin(phi)*cos(phi)+.2212715683*`&epsilon;`^2*sin(phi)*cos(phi)+2.252753163*`&epsilon;`^2*sin(phi)^15*cos(phi)+4.857729947*`&epsilon;`^4*sin(phi)^7*cos(phi)+.2775645236*`&epsilon;`^8*sin(phi)^5*cos(phi)+0.1560418629e-7*`&epsilon;`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+.6645139802*sin(phi)^11*cos(phi)

 

.9885168554*`&epsilon;`^8*sin(phi)^9*cos(phi)+0.1249753779e-2*`&epsilon;`^12*sin(phi)^3*cos(phi)+3.258184644*`&epsilon;`^6*sin(phi)^9*cos(phi)+.1124269022*`&epsilon;`^10*sin(phi)^7*cos(phi)+0.4588193106e-1*`&epsilon;`^10*sin(phi)^5*cos(phi)+.2565381358*`&epsilon;`^4*sin(phi)*cos(phi)+6.282275004*`&epsilon;`^4*sin(phi)^11*cos(phi)+0.4933078791e-5*`&epsilon;`^16*sin(phi)^3*cos(phi)+5.282506255*`&epsilon;`^2*sin(phi)^9*cos(phi)+2.242139502*`&epsilon;`^6*sin(phi)^7*cos(phi)+6.170463035*`&epsilon;`^4*sin(phi)^9*cos(phi)+0.8234222560e-1*`&epsilon;`^8*sin(phi)^3*cos(phi)+0.9608710101e-4*`&epsilon;`^14*sin(phi)^3*cos(phi)+3.656113028*`&epsilon;`^6*sin(phi)^11*cos(phi)+5.222697446*`&epsilon;`^4*sin(phi)^13*cos(phi)+0.1562649478e-2*`&epsilon;`^10*sin(phi)*cos(phi)+.6194422970*`&epsilon;`^8*sin(phi)^7*cos(phi)+3.520102051*`&epsilon;`^2*sin(phi)^13*cos(phi)+0.1186386550e-1*`&epsilon;`^10*sin(phi)^3*cos(phi)+4.689119196*`&epsilon;`^2*sin(phi)^11*cos(phi)+1.375810863*`&epsilon;`^2*sin(phi)^3*cos(phi)+0.4740690151e-6*`&epsilon;`^16*sin(phi)*cos(phi)+0.4077214292e-3*`&epsilon;`^14*sin(phi)^5*cos(phi)+0.9582543506e-5*`&epsilon;`^14*sin(phi)*cos(phi)+0.5349926002e-2*`&epsilon;`^12*sin(phi)^5*cos(phi)+.1742483217*`&epsilon;`^10*sin(phi)^9*cos(phi)+1.148250169*`&epsilon;`^6*sin(phi)^5*cos(phi)+0.1277730241e-1*`&epsilon;`^12*sin(phi)^7*cos(phi)+0.7437311918e-1*`&epsilon;`^6*sin(phi)*cos(phi)+1.080128320*`&epsilon;`^8*sin(phi)^11*cos(phi)+2.975771526*`&epsilon;`^6*sin(phi)^13*cos(phi)+1.134364300*`&epsilon;`^2*sin(phi)^17*cos(phi)+3.293959886*`&epsilon;`^4*sin(phi)^15*cos(phi)+1.168884099*`&epsilon;`^4*sin(phi)^3*cos(phi)+3.270035435*`&epsilon;`^2*sin(phi)^5*cos(phi)+0.1283200926e-1*`&epsilon;`^8*sin(phi)*cos(phi)+4.820745909*`&epsilon;`^2*sin(phi)^7*cos(phi)+.3981616844*`&epsilon;`^6*sin(phi)^3*cos(phi)+2.891022275*`&epsilon;`^4*sin(phi)^5*cos(phi)+0.1414814731e-3*`&epsilon;`^12*sin(phi)*cos(phi)+.2212715683*`&epsilon;`^2*sin(phi)*cos(phi)+2.252753163*`&epsilon;`^2*sin(phi)^15*cos(phi)+4.857729947*`&epsilon;`^4*sin(phi)^7*cos(phi)+.2775645236*`&epsilon;`^8*sin(phi)^5*cos(phi)+0.1560418629e-7*`&epsilon;`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+.6645139802*sin(phi)^11*cos(phi)

 

{phi = 0., `&epsilon;` = `&epsilon;`}, {phi = 1.570796327, `&epsilon;` = `&epsilon;`}, {phi = phi, `&epsilon;` = RootOf(1560418629*_Z^18+(47406901510+493307879100*sin(phi)^2)*_Z^16+(40772142920000*sin(phi)^4+9608710101000*sin(phi)^2+958254350600)*_Z^14+(14148147310000+124975377900000*sin(phi)^2+534992600200000*sin(phi)^4+1277730241000000*sin(phi)^6)*_Z^12+(11242690220000000*sin(phi)^6+1186386550000000*sin(phi)^2+17424832170000000*sin(phi)^8+156264947800000+4588193106000000*sin(phi)^4)*_Z^10+(8234222560000000*sin(phi)^2+61944229700000000*sin(phi)^6+98851685540000000*sin(phi)^8+108012832000000000*sin(phi)^10+27756452360000000*sin(phi)^4+1283200926000000)*_Z^8+(7437311918000000+114825016900000000*sin(phi)^4+297577152600000000*sin(phi)^12+325818464400000000*sin(phi)^8+365611302800000000*sin(phi)^10+224213950200000000*sin(phi)^6+39816168440000000*sin(phi)^2)*_Z^6+(485772994700000000*sin(phi)^6+628227500400000000*sin(phi)^10+522269744600000000*sin(phi)^12+329395988600000000*sin(phi)^14+25653813580000000+617046303500000000*sin(phi)^8+116888409900000000*sin(phi)^2+289102227500000000*sin(phi)^4)*_Z^4+(22127156830000000+137581086300000000*sin(phi)^2+468911919600000000*sin(phi)^10+352010205100000000*sin(phi)^12+225275316300000000*sin(phi)^14+528250625500000000*sin(phi)^8+327003543500000000*sin(phi)^4+113436430000000000*sin(phi)^16+482074590900000000*sin(phi)^6)*_Z^2-62572261930000000-13317339210000000*sin(phi)^2+12655803050000000*sin(phi)^16+54673602200000000*sin(phi)^4+86678520620000000*sin(phi)^8+43371363110000000*sin(phi)^12+66451398020000000*sin(phi)^10+88614086100000000*sin(phi)^6+24941899980000000*sin(phi)^14+5208654259000000*sin(phi)^18)}

 

Error, (in fsolve) number of equations, 1, does not match number of variables, 2

 

``


 

Download equations_solve.mw

I am trying to evaluate the following equation analytically but it gives back unevaluated then I tried fsolve which giving me the answer but I need phi greater than  zero. How can I avoid negative values. Also Is there any ways to solve it analytically. 

Please see the attachment

 

Download ANALYTIC.mw

 

Hi,

I have three simultaneous equations  with three unknown variables (E, W, T). When I solve these  simultaneous equations with fsolve command without specifying any range for variables, I don't get desirable root ( equation sol4 in maple worksheet- {E = 0.1007672475e-2, T = .7969434549, W = 0.1937272759e-2}). For this problem, I know the correct root {E = 2843.916504, T = .2782913990, W = 5344.844134} beforehand which maximize the objective function TP (equation sol8 in maple worksheet) and when I specify the narrow range of variables around the already known correct root in the fsolve command, then I get correct root ( equation sol5 in maple worksheet). If I don't know the actual answer (correct roots of the simultaneous equation) beforehand, How  could I get the correct root with fsolve command because it is very tedious work to specify different range in fsolve command repetitively to solve it by trial and error.

I also tried Direct Search method as suggested in this forum  but DirectSearch is also not able to provide the correct root (equation sol6 in maple worksheet). If I specify the narrow range around known root in direct search method ( equation sol6a in maple worksheet), then it would provide close to optimal root but if I don't know the correct root beforehand, then I couldn't specify the narrow range of variables, then how can I get correct root through direct search command.

Equation sol10 in maple worksheet  (objective function value at correct root) confirms that {E = 2843.916504, T = .2782913990, W = 5344.844134} is the correct root because it provide the value of objective function (TP) equal to 78285.85621 as opposed to negative value (TP value -12.53348074 in equation sol9)  produced by incorrect root  {E = 0.1007672475e-2, T = .7969434549, W = 0.1937272759e-2}).

Is there any method which would provide all the roots of these simultaneous equations which also include correct root. Maple worksheet is attached.

I am trying fsolve and direct search method with known root so that I could get the proper procedure to get the correct root which I can apply to another problem (set of similar simultaneous equations) for which I don't know correct root beforehand.

Thanks for your anticipated help.fsolve_question.mw

Ok, so i have this functions

where f(x) represent urban population and g(x) represent the rural population.

And i have to implement an algortihm in Maple to find out after what period of time x the rural population will be with 20% bigger than urban population.

I'm new in Maple and is a little bit hard for me to implement algorithms in this program.If you can help me with any idea, i will really apreciate.Thank you :). 

Hi, 

I need to solve system of 6 non linear equations. 

Down here you can see the code I wrote and at the end used to fsolve function, and it is not running. I get an error about the const 'V': Error, (in fsolve) V is in the equation, and is not solved for.

What is the right way to solve this system?

Thank you very much!

 

 

omega1 := 1.562;
omega2 := 2.449;
omega3 := 3.325;
y1 := c1*sin(omega1*t+phi1)+c2*sin(omega2*t+phi2)+c3*sin(omega3*t+phi3);

 

 

y2 := .1019*c1*sin(omega1*t+phi1)+.75*c2*sin(omega2*t+phi2)+.4608*c3*sin(omega3*t+phi3);

 

 

y3 := .407*c1*sin(omega1*t+phi1)+(0*c2)*sin(omega2*t+phi2)+1.844*c3*sin(omega3*t+phi3);
 
eq1 := subs(t = 0, y1) = 0;
 
eq2 := subs(t = 0, y2) = 0;
 
eq3 := subs(t = 0, y3) = 0;
 
eq4 := subs(t = 0, diff(y1, t)) = V;
eq5 := subs(t = 0, diff(y2, t)) = 0;
eq6 := subs(t = 0, diff(y3, t)) = 0;

 

 

eqs := [eq1, eq2, eq3, eq4, eq5, eq6];
 
vars := [c1, c2, c3, phi1, phi2, phi3];
 
fsolve({eq1, eq2, eq3, eq4, eq5, eq6}, {c1, c2, c3, phi1, phi2, phi3});
 

 

i have set of equations and variable that i want to solve them using fsolve, but after about 20mintues of computations, fsolve retrun these set unevaluated, could anyone help?


 

 restart:with(linalg):with(LinearAlgebra):with(orthopoly):Digits:=40:
M:=3:
N:=2:
l:=2:
for m from 0 to M-1 do
L[m]:=unapply(P(m,t),t);
end do:
for n from 1 to N do;
for m from 0 to M-1 do;
BB[n,m]:=unapply(piecewise((n-1)/N<=t and t<n/N, sqrt(N*(2*m+1))*L[m](2*N*t-2*n+1)),t);
end do:
end do:
##############################################
B:=Vector(N*M,1,[seq(seq(BB[n,m](t),m=0..M-1),n=1..N)]):
BS:=Vector(N*M,1,[seq(seq(BB[n,m](s),m=0..M-1),n=1..N)]):
f[1]:=unapply((23/35)*t,t):
f[2]:=unapply((11/12)*t,t):
P[1]:=evalf(Vector(N*M,1,[seq(seq(int((23/35)*t*BB[n,m](t),t=0..1,t=0..1),m=0..M-1),n=1..N)])):
P[2]:=evalf(Vector(N*M,1,[seq(seq(int((11/12)*t*BB[n,m](t),t=0..1,t=0..1),m=0..M-1),n=1..N)])):
p[1]:=Transpose(P[1]):P[1]^+:
p[2]:=Transpose(P[2]):P[2]^+:

 

#############################################
k:=Matrix(2,2,[[t*s^2,t*s^2],[s*t^2,s*t^2]]):

 

 

 

 

 

 

 

 

 

######################################

for i from 1 to 2 do;
for j from 1 to 2 do;
T[i,j]:=Matrix(N*M,N*M):

for n from 1 to M*N do;
for m from 1 to M*N do;
T[i,j](n,m):=evalf(int(int(B[n]*k(i,j)*BS[m],t=0..1),s=0..1)):
end do:
end do:
od:
od:
evalm(T[1,1]):
evalm(T[1,2]):
evalm(T[2,1]):
evalm(T[2,2]):

 

 

##########################################

X[1]:=Matrix(M*N,1):
for n from 1 to M*N do;
X[1](n,1):=Y[n,1]:
od:
evalm(X[1]):
#### yadet bashe k dar in mesal majhulat y1,y2
####ba bordarhaye X1, X2 neshun dadi...darvaghe
####dar mesale avale maghale 2ta y dashti k bayad moadele ash ro hal mikardi...
 

 

X[2]:=Matrix(M*N,1):
for n from 1 to M*N do;
X[2](n,1):=yY[n,1]:
od:
evalm(X[2]):

U[1,1]:=Matrix(M*N,1):
for n from 1 to M*N do;
U[1,1](n,1):=u[n,1]:
od:
evalm(U[1,1]):

U[1,2]:=Matrix(M*N,1):
for n from 1 to M*N do;
U[1,2](n,1):=uU[n,1]:
od:

evalm(U[1,2]):
Transpose(U[1,2]):

U[2,1]:=Matrix(N*M,1):
for n from 1 to M*N do;
U[2,1](n,1):=w[n,1]:
od:
evalm(U[2,1]):

U[2,2]:=Matrix(M*N,1):
for n from 1 to M*N do;
U[2,2](n,1):=wW[n,1]:
od:
evalm(U[2,2]):





 


A:=add(X[j], j=1..2):

z[1]:=Matrix(1,M*N):
z[2]:=Matrix(1,M*N):
for i from 1 to 2 do;
Z[i]:=Transpose(A)-add(Transpose(U[i,j]).T[i,j], j=1..2);
evalm(Z[i]):
z[i]:=Z[i]-convert(p[i],Matrix):
od:
evalm(z[1]):
##############
z[1](1,2):


##########################################
for s from 1 to M*N do;
t:=((2*s)-1)/(2*M*N);
ff[1,1]:=eval(VectorMatrixMultiply(Transpose(X[1]),eval(B,t=((2*s)-1)/(2*M*N))));
F[1,s]:=multiply(ff[1,1],ff[1,1]);
expand(%):
H[1,s]:=VectorMatrixMultiply(Transpose(U[1,1]),eval(B,t=((2*s)-1)/(2*M*N)));
hh[1,s]:=F[1,s]-H[1,s][1];
od:

 

ff[1,1]:


 

F[1,1]:

H[1,1]:

hh[1,2]:

 

for s from 1 to M*N do;
t:=((2*s)-1)/(2*M*N);
ff[2,1]:=eval(VectorMatrixMultiply(Transpose(X[1]),eval(B,t=((2*s)-1)/(2*M*N))));
G[1,s]:=multiply(ff[2,1],ff[2,1]);
expand(%):
J[1,s]:=VectorMatrixMultiply(Transpose(U[2,1]),eval(B,t=((2*s)-1)/(2*M*N)));
JJ[1,s]:=G[1,s]-J[1,s][1];
od:
JJ[1,1]:
JJ[1,2]:

for s from 1 to M*N do;
t:=((2*s)-1)/(2*M*N);
ff[1,2]:=eval(VectorMatrixMultiply(Transpose(X[2]),eval(B,t=((2*s)-1)/(2*M*N))));
GG[1,s]:=multiply(ff[1,2],ff[1,2]);
expand(%):
g[1,s]:=VectorMatrixMultiply(Transpose(U[1,2]),eval(B,t=((2*s)-1)/(2*M*N)));
gg[1,s]:=GG[1,s]-g[1,s][1];
od:
gg[1,1]:
gg[1,2]:

for s from 1 to M*N do;
t:=((2*s)-1)/(2*M*N);
ff[2,2]:=eval(VectorMatrixMultiply(Transpose(X[2]),eval(B,t=((2*s)-1)/(2*M*N))));
DD[1,s]:=multiply(ff[2,2],ff[2,2]);
expand(%):
d[1,s]:=VectorMatrixMultiply(Transpose(U[2,2]),eval(B,t=((2*s)-1)/(2*M*N)));
dd[1,s]:=DD[1,s]-d[1,s][1];
od:
dd[1,1]:
dd[1,2]:


eqq[1]:=seq(hh[1,s],s=1..M*N):

eqq[2]:=seq(gg[1,s],s=1..M*N):

 

eqq[3]:=seq(JJ[1,s],s=1..M*N):

eqq[4]:=seq(dd[1,s],s=1..M*N):
eqq[5]:=seq(z[1](1,s),s=1..M*N):
eqq[6]:=seq(z[2](1,s),s=1..M*N):

eq:=seq(eqq[s],s=1..M*N):

var[1]:=seq(X[1](s,1),s=1..M*N):
var[2]:=seq(X[2](s,1),s=1..M*N):
var[3]:=seq(U[1,1](s,1),s=1..M*N):
var[4]:=seq(U[1,2](s,1),s=1..M*N):
var[5]:=seq(U[2,1](s,1),s=1..M*N):
var[6]:=seq(U[2,2](s,1),s=1..M*N):

EQ:=Matrix(36,1):

for i to 6 do
EQ(6*i-5,1):=hh[1,i];
EQ(6*i-4,1):=gg[1,i];
EQ(6*i-3,1):=JJ[1,i];
EQ(6*i-2,1):=dd[1,i];
EQ(6*i-1,1):=z[1](1,i);
EQ(6*i,1):=z[2](1,i);
od:

 

indets(EQ);

{Y[1, 1], Y[2, 1], Y[3, 1], Y[4, 1], Y[5, 1], Y[6, 1], u[1, 1], u[2, 1], u[3, 1], u[4, 1], u[5, 1], u[6, 1], uU[1, 1], uU[2, 1], uU[3, 1], uU[4, 1], uU[5, 1], uU[6, 1], w[1, 1], w[2, 1], w[3, 1], w[4, 1], w[5, 1], w[6, 1], wW[1, 1], wW[2, 1], wW[3, 1], wW[4, 1], wW[5, 1], wW[6, 1], yY[1, 1], yY[2, 1], yY[3, 1], yY[4, 1], yY[5, 1], yY[6, 1]}

(1)

``

``

Var:=[seq](var[s],s=1..M*N);

[Y[1, 1], Y[2, 1], Y[3, 1], Y[4, 1], Y[5, 1], Y[6, 1], yY[1, 1], yY[2, 1], yY[3, 1], yY[4, 1], yY[5, 1], yY[6, 1], u[1, 1], u[2, 1], u[3, 1], u[4, 1], u[5, 1], u[6, 1], uU[1, 1], uU[2, 1], uU[3, 1], uU[4, 1], uU[5, 1], uU[6, 1], w[1, 1], w[2, 1], w[3, 1], w[4, 1], w[5, 1], w[6, 1], wW[1, 1], wW[2, 1], wW[3, 1], wW[4, 1], wW[5, 1], wW[6, 1]]

(2)

seq(indets(EQ[i][1]), i = 1 .. 36):

``

``

 

for i to 36 do
EQQ[i]:=simplify(expand(subs([seq](indets(EQ)[i]=AA[i],i=1..36),EQ[i][1])=0));
od;

(1/18)*(12*AA[8]*3^(1/2)-3*AA[9]*5^(1/2)-18*AA[7])*2^(1/2)-(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0

 

(1/18)*(12*AA[14]*3^(1/2)-3*AA[15]*5^(1/2)-18*AA[13])*2^(1/2)-(8/3)*((1/6)*AA[33]*5^(1/2)+AA[31])*AA[32]*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0

 

(1/18)*(12*AA[20]*3^(1/2)-3*AA[21]*5^(1/2)-18*AA[19])*2^(1/2)-(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0

 

(1/18)*(12*AA[26]*3^(1/2)-3*AA[27]*5^(1/2)-18*AA[25])*2^(1/2)-(8/3)*((1/6)*AA[33]*5^(1/2)+AA[31])*AA[32]*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0

 

AA[1]+AA[31]-0.1041666666666666666666666666666666666667e-1*AA[7]-0.6014065304058601713636966463562056829663e-2*AA[8]-0.3125000000000000000000000000000000000000e-1*AA[10]-0.6014065304058601713636966463562056829663e-2*AA[11]-0.1041666666666666666666666666666666666667e-1*AA[13]-0.6014065304058601713636966463562056829663e-2*AA[14]-0.3125000000000000000000000000000000000000e-1*AA[16]-0.6014065304058601713636966463562056829663e-2*AA[17]-.1161675426235042361515672880600823421682 = 0

 

AA[1]+AA[31]-0.1041666666666666666666666666666666666667e-1*AA[19]-0.9021097956087902570455449695343085244494e-2*AA[20]-0.2329237476562280933759555904928412745252e-2*AA[21]-0.7291666666666666666666666666666666666667e-1*AA[22]-0.2706329386826370771136634908602925573348e-1*AA[23]-0.2329237476562280933759555904928412745252e-2*AA[24]-0.1041666666666666666666666666666666666667e-1*AA[25]-0.9021097956087902570455449695343085244494e-2*AA[26]-0.2329237476562280933759555904928412745252e-2*AA[27]-0.7291666666666666666666666666666666666667e-1*AA[28]-0.2706329386826370771136634908602925573348e-1*AA[29]-0.2329237476562280933759555904928412745252e-2*AA[30]-.1620453040219171410085268329823612381694 = 0

 

(1/2)*(AA[9]*5^(1/2)-2*AA[7])*2^(1/2)-2*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(5/2)*AA[3]^2 = 0

 

(1/2)*(AA[15]*5^(1/2)-2*AA[13])*2^(1/2)-2*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(5/2)*AA[33]^2 = 0

 

(1/2)*(AA[21]*5^(1/2)-2*AA[19])*2^(1/2)-2*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(5/2)*AA[3]^2 = 0

 

(1/2)*(AA[27]*5^(1/2)-2*AA[25])*2^(1/2)-2*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(5/2)*AA[33]^2 = 0

 

AA[2]+AA[32]-0.9021097956087902570455449695343085244494e-2*AA[7]-0.5208333333333333333333333333333333333333e-2*AA[8]-0.2706329386826370771136634908602925573348e-1*AA[10]-0.5208333333333333333333333333333333333333e-2*AA[11]-0.9021097956087902570455449695343085244494e-2*AA[13]-0.5208333333333333333333333333333333333333e-2*AA[14]-0.2706329386826370771136634908602925573348e-1*AA[16]-0.5208333333333333333333333333333333333333e-2*AA[17]-0.6706936200477749554587801633123274049430e-1 = 0

 

AA[2]+AA[32]-0.6014065304058601713636966463562056829663e-2*AA[19]-0.5208333333333333333333333333333333333333e-2*AA[20]-0.1344785884099797529576133819368888753762e-2*AA[21]-0.4209845712841021199545876524493439780765e-1*AA[22]-0.1562500000000000000000000000000000000000e-1*AA[23]-0.1344785884099797529576133819368888753762e-2*AA[24]-0.6014065304058601713636966463562056829663e-2*AA[25]-0.5208333333333333333333333333333333333333e-2*AA[26]-0.1344785884099797529576133819368888753762e-2*AA[27]-0.4209845712841021199545876524493439780765e-1*AA[28]-0.1562500000000000000000000000000000000000e-1*AA[29]-0.1344785884099797529576133819368888753762e-2*AA[30]-0.9355689989796860791725737785335001844313e-1 = 0

 

(1/18)*(-12*AA[8]*3^(1/2)-3*AA[9]*5^(1/2)-18*AA[7])*2^(1/2)+(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0

 

(1/18)*(-12*AA[14]*3^(1/2)-3*AA[15]*5^(1/2)-18*AA[13])*2^(1/2)+(8/3)*((1/6)*AA[33]*5^(1/2)+AA[31])*AA[32]*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0

 

(1/18)*(-12*AA[20]*3^(1/2)-3*AA[21]*5^(1/2)-18*AA[19])*2^(1/2)+(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0

 

(1/18)*(-12*AA[26]*3^(1/2)-3*AA[27]*5^(1/2)-18*AA[25])*2^(1/2)+(8/3)*((1/6)*AA[33]*5^(1/2)+AA[31])*AA[32]*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0

 

AA[3]+AA[33]-0.2329237476562280933759555904928412745252e-2*AA[7]-0.1344785884099797529576133819368888753762e-2*AA[8]-0.6987712429686842801278667714785238235753e-2*AA[10]-0.1344785884099797529576133819368888753762e-2*AA[11]-0.2329237476562280933759555904928412745252e-2*AA[13]-0.1344785884099797529576133819368888753762e-2*AA[14]-0.6987712429686842801278667714785238235753e-2*AA[16]-0.1344785884099797529576133819368888753762e-2*AA[17] = 0

 

AA[3]+AA[33] = 0

 

(1/18)*(12*AA[11]*3^(1/2)-3*AA[12]*5^(1/2)-18*AA[10])*2^(1/2)-(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0

 

(1/18)*(12*AA[17]*3^(1/2)-3*AA[18]*5^(1/2)-18*AA[16])*2^(1/2)-(8/3)*((1/6)*AA[36]*5^(1/2)+AA[34])*AA[35]*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0

 

(1/18)*(12*AA[23]*3^(1/2)-3*AA[24]*5^(1/2)-18*AA[22])*2^(1/2)-(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0

 

(1/18)*(12*AA[29]*3^(1/2)-3*AA[30]*5^(1/2)-18*AA[28])*2^(1/2)-(8/3)*((1/6)*AA[36]*5^(1/2)+AA[34])*AA[35]*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0

 

AA[4]+AA[34]-0.7291666666666666666666666666666666666667e-1*AA[7]-0.4209845712841021199545876524493439780765e-1*AA[8]-.2187500000000000000000000000000000000000*AA[10]-0.4209845712841021199545876524493439780765e-1*AA[11]-0.7291666666666666666666666666666666666667e-1*AA[13]-0.4209845712841021199545876524493439780765e-1*AA[14]-.2187500000000000000000000000000000000000*AA[16]-0.4209845712841021199545876524493439780765e-1*AA[17]-.3485026278705127084547018641802470265047 = 0

 

AA[4]+AA[34]-0.3125000000000000000000000000000000000000e-1*AA[19]-0.2706329386826370771136634908602925573348e-1*AA[20]-0.6987712429686842801278667714785238235753e-2*AA[21]-.2187500000000000000000000000000000000000*AA[22]-0.8118988160479112313409904725808776720045e-1*AA[23]-0.6987712429686842801278667714785238235753e-2*AA[24]-0.3125000000000000000000000000000000000000e-1*AA[25]-0.2706329386826370771136634908602925573348e-1*AA[26]-0.6987712429686842801278667714785238235753e-2*AA[27]-.2187500000000000000000000000000000000000*AA[28]-0.8118988160479112313409904725808776720045e-1*AA[29]-0.6987712429686842801278667714785238235753e-2*AA[30]-.4861359120657514230255804989470837145084 = 0

 

(1/2)*(AA[12]*5^(1/2)-2*AA[10])*2^(1/2)-2*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(5/2)*AA[6]^2 = 0

 

(1/2)*(AA[18]*5^(1/2)-2*AA[16])*2^(1/2)-2*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(5/2)*AA[36]^2 = 0

 

(1/2)*(AA[24]*5^(1/2)-2*AA[22])*2^(1/2)-2*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(5/2)*AA[6]^2 = 0

 

(1/2)*(AA[30]*5^(1/2)-2*AA[28])*2^(1/2)-2*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(5/2)*AA[36]^2 = 0

 

AA[5]+AA[35]-0.2706329386826370771136634908602925573348e-1*AA[7]-0.1562500000000000000000000000000000000000e-1*AA[8]-0.8118988160479112313409904725808776720045e-1*AA[10]-0.1562500000000000000000000000000000000000e-1*AA[11]-0.2706329386826370771136634908602925573348e-1*AA[13]-0.1562500000000000000000000000000000000000e-1*AA[14]-0.8118988160479112313409904725808776720045e-1*AA[16]-0.1562500000000000000000000000000000000000e-1*AA[17]-0.6706936200477749554587801633123274049430e-1 = 0

 

AA[5]+AA[35]-0.6014065304058601713636966463562056829663e-2*AA[19]-0.5208333333333333333333333333333333333333e-2*AA[20]-0.1344785884099797529576133819368888753762e-2*AA[21]-0.4209845712841021199545876524493439780765e-1*AA[22]-0.1562500000000000000000000000000000000000e-1*AA[23]-0.1344785884099797529576133819368888753762e-2*AA[24]-0.6014065304058601713636966463562056829663e-2*AA[25]-0.5208333333333333333333333333333333333333e-2*AA[26]-0.1344785884099797529576133819368888753762e-2*AA[27]-0.4209845712841021199545876524493439780765e-1*AA[28]-0.1562500000000000000000000000000000000000e-1*AA[29]-0.1344785884099797529576133819368888753762e-2*AA[30]-0.9355689989796860791725737785335001844313e-1 = 0

 

(1/18)*(-12*AA[11]*3^(1/2)-3*AA[12]*5^(1/2)-18*AA[10])*2^(1/2)+(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0

 

(1/18)*(-12*AA[17]*3^(1/2)-3*AA[18]*5^(1/2)-18*AA[16])*2^(1/2)+(8/3)*((1/6)*AA[36]*5^(1/2)+AA[34])*AA[35]*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0

 

(1/18)*(-12*AA[23]*3^(1/2)-3*AA[24]*5^(1/2)-18*AA[22])*2^(1/2)+(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0

 

(1/18)*(-12*AA[29]*3^(1/2)-3*AA[30]*5^(1/2)-18*AA[28])*2^(1/2)+(8/3)*((1/6)*AA[36]*5^(1/2)+AA[34])*AA[35]*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0

 

AA[6]+AA[36]-0.2329237476562280933759555904928412745252e-2*AA[7]-0.1344785884099797529576133819368888753762e-2*AA[8]-0.6987712429686842801278667714785238235753e-2*AA[10]-0.1344785884099797529576133819368888753762e-2*AA[11]-0.2329237476562280933759555904928412745252e-2*AA[13]-0.1344785884099797529576133819368888753762e-2*AA[14]-0.6987712429686842801278667714785238235753e-2*AA[16]-0.1344785884099797529576133819368888753762e-2*AA[17] = 0

 

AA[6]+AA[36] = 0

(3)

fsolve({seq}(EQQ[i],i=1..36),{seq}(AA[i],i=1..36));

fsolve({AA[3]+AA[33] = 0, AA[6]+AA[36] = 0, (1/2)*(AA[9]*5^(1/2)-2*AA[7])*2^(1/2)-2*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(5/2)*AA[3]^2 = 0, (1/2)*(AA[12]*5^(1/2)-2*AA[10])*2^(1/2)-2*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(5/2)*AA[6]^2 = 0, (1/2)*(AA[15]*5^(1/2)-2*AA[13])*2^(1/2)-2*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(5/2)*AA[33]^2 = 0, (1/2)*(AA[18]*5^(1/2)-2*AA[16])*2^(1/2)-2*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(5/2)*AA[36]^2 = 0, (1/2)*(AA[21]*5^(1/2)-2*AA[19])*2^(1/2)-2*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(5/2)*AA[3]^2 = 0, (1/2)*(AA[24]*5^(1/2)-2*AA[22])*2^(1/2)-2*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(5/2)*AA[6]^2 = 0, (1/2)*(AA[27]*5^(1/2)-2*AA[25])*2^(1/2)-2*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(5/2)*AA[33]^2 = 0, (1/2)*(AA[30]*5^(1/2)-2*AA[28])*2^(1/2)-2*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(5/2)*AA[36]^2 = 0, (1/18)*(-12*AA[8]*3^(1/2)-3*AA[9]*5^(1/2)-18*AA[7])*2^(1/2)+(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0, (1/18)*(12*AA[8]*3^(1/2)-3*AA[9]*5^(1/2)-18*AA[7])*2^(1/2)-(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0, (1/18)*(-12*AA[11]*3^(1/2)-3*AA[12]*5^(1/2)-18*AA[10])*2^(1/2)+(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0, (1/18)*(12*AA[11]*3^(1/2)-3*AA[12]*5^(1/2)-18*AA[10])*2^(1/2)-(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0, (1/18)*(-12*AA[14]*3^(1/2)-3*AA[15]*5^(1/2)-18*AA[13])*2^(1/2)+(8/3)*AA[32]*((1/6)*AA[33]*5^(1/2)+AA[31])*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0, (1/18)*(12*AA[14]*3^(1/2)-3*AA[15]*5^(1/2)-18*AA[13])*2^(1/2)-(8/3)*AA[32]*((1/6)*AA[33]*5^(1/2)+AA[31])*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0, (1/18)*(-12*AA[17]*3^(1/2)-3*AA[18]*5^(1/2)-18*AA[16])*2^(1/2)+(8/3)*AA[35]*((1/6)*AA[36]*5^(1/2)+AA[34])*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0, (1/18)*(12*AA[17]*3^(1/2)-3*AA[18]*5^(1/2)-18*AA[16])*2^(1/2)-(8/3)*AA[35]*((1/6)*AA[36]*5^(1/2)+AA[34])*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0, (1/18)*(-12*AA[20]*3^(1/2)-3*AA[21]*5^(1/2)-18*AA[19])*2^(1/2)+(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0, (1/18)*(12*AA[20]*3^(1/2)-3*AA[21]*5^(1/2)-18*AA[19])*2^(1/2)-(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0, (1/18)*(-12*AA[23]*3^(1/2)-3*AA[24]*5^(1/2)-18*AA[22])*2^(1/2)+(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0, (1/18)*(12*AA[23]*3^(1/2)-3*AA[24]*5^(1/2)-18*AA[22])*2^(1/2)-(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0, (1/18)*(-12*AA[26]*3^(1/2)-3*AA[27]*5^(1/2)-18*AA[25])*2^(1/2)+(8/3)*AA[32]*((1/6)*AA[33]*5^(1/2)+AA[31])*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0, (1/18)*(12*AA[26]*3^(1/2)-3*AA[27]*5^(1/2)-18*AA[25])*2^(1/2)-(8/3)*AA[32]*((1/6)*AA[33]*5^(1/2)+AA[31])*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0, (1/18)*(-12*AA[29]*3^(1/2)-3*AA[30]*5^(1/2)-18*AA[28])*2^(1/2)+(8/3)*AA[35]*((1/6)*AA[36]*5^(1/2)+AA[34])*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0, (1/18)*(12*AA[29]*3^(1/2)-3*AA[30]*5^(1/2)-18*AA[28])*2^(1/2)-(8/3)*AA[35]*((1/6)*AA[36]*5^(1/2)+AA[34])*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0, AA[3]+AA[33]-0.2329237476562280933759555904928412745252e-2*AA[7]-0.1344785884099797529576133819368888753762e-2*AA[8]-0.6987712429686842801278667714785238235753e-2*AA[10]-0.1344785884099797529576133819368888753762e-2*AA[11]-0.2329237476562280933759555904928412745252e-2*AA[13]-0.1344785884099797529576133819368888753762e-2*AA[14]-0.6987712429686842801278667714785238235753e-2*AA[16]-0.1344785884099797529576133819368888753762e-2*AA[17] = 0, AA[6]+AA[36]-0.2329237476562280933759555904928412745252e-2*AA[7]-0.1344785884099797529576133819368888753762e-2*AA[8]-0.6987712429686842801278667714785238235753e-2*AA[10]-0.1344785884099797529576133819368888753762e-2*AA[11]-0.2329237476562280933759555904928412745252e-2*AA[13]-0.1344785884099797529576133819368888753762e-2*AA[14]-0.6987712429686842801278667714785238235753e-2*AA[16]-0.1344785884099797529576133819368888753762e-2*AA[17] = 0, AA[1]+AA[31]-0.1041666666666666666666666666666666666667e-1*AA[7]-0.6014065304058601713636966463562056829663e-2*AA[8]-0.3125000000000000000000000000000000000000e-1*AA[10]-0.6014065304058601713636966463562056829663e-2*AA[11]-0.1041666666666666666666666666666666666667e-1*AA[13]-0.6014065304058601713636966463562056829663e-2*AA[14]-0.3125000000000000000000000000000000000000e-1*AA[16]-0.6014065304058601713636966463562056829663e-2*AA[17]-.1161675426235042361515672880600823421682 = 0, AA[2]+AA[32]-0.9021097956087902570455449695343085244494e-2*AA[7]-0.5208333333333333333333333333333333333333e-2*AA[8]-0.2706329386826370771136634908602925573348e-1*AA[10]-0.5208333333333333333333333333333333333333e-2*AA[11]-0.9021097956087902570455449695343085244494e-2*AA[13]-0.5208333333333333333333333333333333333333e-2*AA[14]-0.2706329386826370771136634908602925573348e-1*AA[16]-0.5208333333333333333333333333333333333333e-2*AA[17]-0.6706936200477749554587801633123274049430e-1 = 0, AA[4]+AA[34]-0.7291666666666666666666666666666666666667e-1*AA[7]-0.4209845712841021199545876524493439780765e-1*AA[8]-.2187500000000000000000000000000000000000*AA[10]-0.4209845712841021199545876524493439780765e-1*AA[11]-0.7291666666666666666666666666666666666667e-1*AA[13]-0.4209845712841021199545876524493439780765e-1*AA[14]-.2187500000000000000000000000000000000000*AA[16]-0.4209845712841021199545876524493439780765e-1*AA[17]-.3485026278705127084547018641802470265047 = 0, AA[5]+AA[35]-0.2706329386826370771136634908602925573348e-1*AA[7]-0.1562500000000000000000000000000000000000e-1*AA[8]-0.8118988160479112313409904725808776720045e-1*AA[10]-0.1562500000000000000000000000000000000000e-1*AA[11]-0.2706329386826370771136634908602925573348e-1*AA[13]-0.1562500000000000000000000000000000000000e-1*AA[14]-0.8118988160479112313409904725808776720045e-1*AA[16]-0.1562500000000000000000000000000000000000e-1*AA[17]-0.6706936200477749554587801633123274049430e-1 = 0, AA[1]+AA[31]-0.1041666666666666666666666666666666666667e-1*AA[19]-0.9021097956087902570455449695343085244494e-2*AA[20]-0.2329237476562280933759555904928412745252e-2*AA[21]-0.7291666666666666666666666666666666666667e-1*AA[22]-0.2706329386826370771136634908602925573348e-1*AA[23]-0.2329237476562280933759555904928412745252e-2*AA[24]-0.1041666666666666666666666666666666666667e-1*AA[25]-0.9021097956087902570455449695343085244494e-2*AA[26]-0.2329237476562280933759555904928412745252e-2*AA[27]-0.7291666666666666666666666666666666666667e-1*AA[28]-0.2706329386826370771136634908602925573348e-1*AA[29]-0.2329237476562280933759555904928412745252e-2*AA[30]-.1620453040219171410085268329823612381694 = 0, AA[2]+AA[32]-0.6014065304058601713636966463562056829663e-2*AA[19]-0.5208333333333333333333333333333333333333e-2*AA[20]-0.1344785884099797529576133819368888753762e-2*AA[21]-0.4209845712841021199545876524493439780765e-1*AA[22]-0.1562500000000000000000000000000000000000e-1*AA[23]-0.1344785884099797529576133819368888753762e-2*AA[24]-0.6014065304058601713636966463562056829663e-2*AA[25]-0.5208333333333333333333333333333333333333e-2*AA[26]-0.1344785884099797529576133819368888753762e-2*AA[27]-0.4209845712841021199545876524493439780765e-1*AA[28]-0.1562500000000000000000000000000000000000e-1*AA[29]-0.1344785884099797529576133819368888753762e-2*AA[30]-0.9355689989796860791725737785335001844313e-1 = 0, AA[4]+AA[34]-0.3125000000000000000000000000000000000000e-1*AA[19]-0.2706329386826370771136634908602925573348e-1*AA[20]-0.6987712429686842801278667714785238235753e-2*AA[21]-.2187500000000000000000000000000000000000*AA[22]-0.8118988160479112313409904725808776720045e-1*AA[23]-0.6987712429686842801278667714785238235753e-2*AA[24]-0.3125000000000000000000000000000000000000e-1*AA[25]-0.2706329386826370771136634908602925573348e-1*AA[26]-0.6987712429686842801278667714785238235753e-2*AA[27]-.2187500000000000000000000000000000000000*AA[28]-0.8118988160479112313409904725808776720045e-1*AA[29]-0.6987712429686842801278667714785238235753e-2*AA[30]-.4861359120657514230255804989470837145084 = 0, AA[5]+AA[35]-0.6014065304058601713636966463562056829663e-2*AA[19]-0.5208333333333333333333333333333333333333e-2*AA[20]-0.1344785884099797529576133819368888753762e-2*AA[21]-0.4209845712841021199545876524493439780765e-1*AA[22]-0.1562500000000000000000000000000000000000e-1*AA[23]-0.1344785884099797529576133819368888753762e-2*AA[24]-0.6014065304058601713636966463562056829663e-2*AA[25]-0.5208333333333333333333333333333333333333e-2*AA[26]-0.1344785884099797529576133819368888753762e-2*AA[27]-0.4209845712841021199545876524493439780765e-1*AA[28]-0.1562500000000000000000000000000000000000e-1*AA[29]-0.1344785884099797529576133819368888753762e-2*AA[30]-0.9355689989796860791725737785335001844313e-1 = 0}, {AA[1], AA[2], AA[3], AA[4], AA[5], AA[6], AA[7], AA[8], AA[9], AA[10], AA[11], AA[12], AA[13], AA[14], AA[15], AA[16], AA[17], AA[18], AA[19], AA[20], AA[21], AA[22], AA[23], AA[24], AA[25], AA[26], AA[27], AA[28], AA[29], AA[30], AA[31], AA[32], AA[33], AA[34], AA[35], AA[36]})

(4)

``


 

Download ttttt33.mw

I am trying to do fsolve in a range (-7..14), however, it gives no solution.

But when I solve the same equations with solve (after removing all the Imaginary solutions), I get two results, one of them is in the range (-7..14). 

I even expanded the range of fsolve, say (-10..20), but still got no solution...

This is just getting weirder and weirder. Attached kindly find the Maple file, note that the first solve takes about 1 minute (on my laptop: CPU i7 + MEM 8G + SSD).

fsolve_In_Range.mw

Hi everybody,

I have to solve a system  of 3 equations in 3 unknowns.
One equation is linear while the others are not because of some  sinh(cste*unknown) term.
More of this the unknowns must verify some constraints of inequality type (but always very simple ; for instance “unknown <= value”).

solve fails because of the sinh terms
fsolve fails due to the inequalities


What Maple procedure do you advise me to use to solve this system ?
(at this stage I think advices could be sufficient ; if I keep coming up against the problem I will submit you a more detailed question)


Thanks in advance

 

With the following command I can plot two spheres and plot them.

f1 := x^2+y^2+z^2 = 1

f2 := x+y+z = 1

with(plottools);

with(plots);

S1 := implicitplot3d(f1, x = -1 .. 1, y = -1 .. 1, z = -1 .. 1, style = patchnogrid, color = blue, scaling = constrained, axes = boxed)

S2 := implicitplot3d(f2, x = -1 .. 1, y = -1 .. 1, z = -1 .. 1, style = patchnogrid, color = gold, scaling = constrained, axes = boxed)

dispaly(S1,S2)

My questions are:

1- How can I display (highlight) the circle which is the intersection between these two sphere on the same figure?

2- How can I find the equation of this circle?

Thank you.

Hi

 

I have a system of equations (4) which I would like to plot in regards to a fifth variable. Is there a good way to do this. Some of the solutions would end up as negative values, which is not an option I am interested in having.

 

C__A is my variable, and the other variables I would like to solve are tau,C__B,C__C,C__D. Im specifically interested in tau with regards to C__A. I hope this makes sense :)

regards

 

C__A := .75;
                              0.75


a := tau = (C__A0-C__A)/(-r__A);
                                  0.75                      
    tau = - ------------------------------------------------
                                              2             
            -0.00900 C__B + 0.03500000000 C__C  - 0.075 C__C
b := tau = (C__B0-C__B)/(-r__B);
                               2 - C__B              
          tau = - -----------------------------------
                                                    2
                  -0.00900 C__B + 0.03500000000 C__C 
c := tau = (C__C0-C__C)/(-r__C);
                                C__C                  
         tau = ---------------------------------------
                                        2             
               0.01800 C__B - 0.070 C__C  - 0.075 C__C
d := tau = (C__D0-C__D)/(-r__D);
                           13.33333333 C__D
                     tau = ----------------
                                 C__C      
sol := fsolve([a, b, c, d], {C__B = 1, C__C = .2, C__D = .2, tau = 50});

{C__B = 1.673672109, C__C = 0.2289836744, C__D = 0.4236721086, 

  tau = 24.66971264}

 

I've encountered a very strange issue with Maple.

The result returns differently with solve and fsolve after/before a variable is given a certain value. See attachment.

The result comes from solve (with variable epsilon) returns value of the same variable with imaginary part while the fsolve returns the correct answer.

Now how can I achieve the same result as fsolve via solve?

Thanks!

Maple_Question_Solve_Fsolve.mw

Maple_Question_Solve_Fsolve.pdf  (exported PDF from Maple)

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