Maple 16 Questions and Posts

These are Posts and Questions associated with the product, Maple 16

Hi Guys,

I am trying to intgrate a function involving hyperbolic functions in a range of 0 to 1 and it is giving me very large value of 10^94. However, on doing integration terms terms i can see that some large terms involving 10^191 cancel out with each other and I can have a fnite value of this integration. It would be really helpful if someone can help me out why it is happening with int function and how can I solve this case involving hyperbolic function. For reference maple file is attached. Thanks in advance and much appreciated.

With Regards

Sunit

question.mw

Hi Guys,

I need help regarding simplifying definite integrals. I have following expression

2*s^2*(int(Phi[1, 1](x, T[2])*(diff(Y1(x), x, x)), x = 0 .. x1))+int(Phi[1, 1](x, T[2])*(diff(Y1(x), x, x, x, x)), x = 0 .. x1)-omega_y^2*(int(Y1(x)*Phi[1, 1](x, T[2]), x = 0 .. x1))

As we can notice the limit for each integral is same, so I should be able to take these integral limit outside. I am trying to use collect and simplify, but both of these command are not working. It would be really helpful for me if I can get the solution for it.

Please find the attached example sheet also.example.mw

With Regards

Sunit

 

Hi Guys,

It might be a very basic question, but I am struggling with it for a quite a time.  I have an expression in a form of

f(x)=h(x)+g(x);

and I want to use factor operation elementwise, i.e., it can individually act on h(x) and can give me

f(x)=h1(x)*h2(x)+g1(x)*g2(x). But whenever I am putting factor operation with elementwise it is not giving me desired answer. It would be really helpful and great if someone can help me out.

I am attaching maple sheet for reference also.

Thanks in advance and regards

Sunit.
example.mw
Download example.mw

 

How do I find integer solutions to this non-linear equation:

 

8= 7(x^2+y^2+z^2)+2x+4y-8z.

 

Tried isolve and it wasn't working. (I guess too many variables?)

 

Also, if f(x,y,z) is the RHS, how do I write a loop that finds integer solutions to f(x,y,z)=c for |x|,|y|,|z|< N, say?

Hello,

I don't understand why Maple gives me the following error:

Error, (in fsolve/Iterators) unrecognized form

The full maple file:


 

restart

mbal := 0.28e-2:

rbal := 0.2e-1:

Cw := .47:

g := 9.81:

A := Pi*rbal^2:

beta := 3.33*Pi*(1/180):

s0x := .2:

s0y := .25:

rho := 1.293:

l := 2:

vx := diff(sx(t), t);

diff(sx(t), t)

(1)

vy := diff(sy(t), t);

diff(sy(t), t)

(2)

ax := diff(sx(t), `$`(t, 2));

diff(diff(sx(t), t), t)

(3)

ay := diff(sy(t), `$`(t, 2));

diff(diff(sy(t), t), t)

(4)

v0x := cos(beta)*v0;

cos(0.1850000000e-1*Pi)*v0

(5)

v0y := sin(beta)*v0;

sin(0.1850000000e-1*Pi)*v0

(6)

`&Sigma;Fx` := -Fdx = mbal*ax;

-Fdx = 0.28e-2*(diff(diff(sx(t), t), t))

(7)

`&Sigma;Fy` := -Fz-Fdy = mbal*ay;

-Fz-Fdy = 0.28e-2*(diff(diff(sy(t), t), t))

(8)

Fz := mbal*g;

0.27468e-1

(9)

Fdx := .5*rho*vx^2*A*Cw;

0.1215420e-3*(diff(sx(t), t))^2*Pi

(10)

Fdy := .5*rho*vy^2*A*Cw;

0.1215420e-3*(diff(sy(t), t))^2*Pi

(11)

ics1 := sx(0) = s0x, (D(sx))(0) = v0x;

sx(0) = .2, (D(sx))(0) = cos(0.1850000000e-1*Pi)*v0

(12)

ics2 := sy(0) = s0y, (D(sy))(0) = v0y;

sy(0) = .25, (D(sy))(0) = sin(0.1850000000e-1*Pi)*v0

(13)

verplaatsingx := dsolve({ics1, `&Sigma;Fx`}, sx(t));

sx(t) = (1400000/60771)*ln((60771/1400000)*cos((37/2000)*Pi)*v0*exp((60771/7000000)*Pi)*t*Pi+exp((60771/7000000)*Pi))/Pi

(14)

verplaatsingy := dsolve({ics2, `&Sigma;Fy`});

sy(t) = (1/243084)*(60771*Pi+2800000*ln((1/92736546000)*(20257*Pi^(1/2)*sin((37/2000)*Pi)*v0*sin((3/70000)*231841365^(1/2)*Pi^(1/2)*t)+20*231841365^(1/2)*cos((3/70000)*231841365^(1/2)*Pi^(1/2)*t))^2))/Pi

(15)

eindy := rhs(verplaatsingy) = rbal;

(1/243084)*(60771*Pi+2800000*ln((1/92736546000)*(20257*Pi^(1/2)*sin((37/2000)*Pi)*v0*sin((3/70000)*231841365^(1/2)*Pi^(1/2)*t)+20*231841365^(1/2)*cos((3/70000)*231841365^(1/2)*Pi^(1/2)*t))^2))/Pi = 0.2e-1

(16)

eindx := rhs(verplaatsingx) = l;

(1400000/60771)*ln((60771/1400000)*cos((37/2000)*Pi)*v0*exp((60771/7000000)*Pi)*t*Pi+exp((60771/7000000)*Pi))/Pi = 2

(17)

t := solve(eindy, t);

RootOf(1397733*Pi+70000000*ln((1/92736546000)*(20257*Pi^(1/2)*sin((37/2000)*Pi)*v0*sin((3/70000)*231841365^(1/2)*Pi^(1/2)*_Z)+20*231841365^(1/2)*cos((3/70000)*231841365^(1/2)*Pi^(1/2)*_Z))^2))

(18)

t := evalf(t[1]);

RootOf(1397733*Pi+70000000*ln((1/92736546000)*(20257*Pi^(1/2)*sin((37/2000)*Pi)*v0*sin((3/70000)*231841365^(1/2)*Pi^(1/2)*_Z)+20*231841365^(1/2)*cos((3/70000)*231841365^(1/2)*Pi^(1/2)*_Z))^2))[1]

(19)

v0 := fsolve(eindx, v0)

Error, (in fsolve/Iterators) unrecognized form

 

``

``


 

Download ttbuddymaple.mw

 

Thank you!

 

How do I draw three vectors on the same axis of coordinates, I see this vector appear after the previous vector one second  and on the screen when this vector appears, the previous vector remains on the screen and on the last screen I see all three vectors with the Maple command?

Example : plottools :- arrow( [1, -2], [4, -1], 0.001, 0.05, 0.1), plottools :- arrow( [-1, 3], [2, 1], 0.001, 0.05, 0.1), plottools :- arrow( [0, 2], [-3, 0], 0.001, 0.05, 0.1).

Thanks so much for the help of everyone!

How do I draw three graphs on the same axis of coordinates and I see this graph appear after the previous graph one second with the Maple command? Example : y = x, y = x2, y = 1 - x.

Thanks so much for the help of everyone!

Lecture 4 - Problem 2
a)
> a := -2100; b := 2100; N := 8; h := (b-a)/N; C := 4491; x := [seq(h, h = -2100 .. 2100, h)]; y := proc (x) options operator, arrow; sqrt(1+((1/2)*exp(x/C)-(1/2)*exp(-x/C))^2) end proc; evalf(y(x[1])); evalf(y(x[N+1])); L := (1/3)*h*(y(x[1])+4*(y(x[2])+y(x[4])+y(x[6])+y(x[N]))+2*(y(x[3])+y(x[5])+y(x[N-1]))+y(x[N+1])); evalf(L);
                             -2100
                              2100
                               8
                              525
                              4491
     [-2100, -1575, -1050, -525, 0, 525, 1050, 1575, 2100]
         /                           2\
         |    /1    /x\   1    /  x\\ |
x -> sqrt|1 + |- exp|-| - - exp|- -|| |
         \    \2    \C/   2    \  C// /
                          1.111332350
                          1.111332350
                                           (1/2)
         /                               2\    
         |    /1    /-700\   1    /700 \\ |    
     175 |1 + |- exp|----| - - exp|----|| |    
         \    \2    \1497/   2    \1497// /     

                                               (1/2)
              /                              2\    
              |    /1    /-175\   1    /175\\ |    
        + 700 |1 + |- exp|----| - - exp|---|| |    
              \    \2    \499 /   2    \499// /     

                                                (1/2)
              /                               2\    
              |    /1    /-175\   1    /175 \\ |    
        + 700 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /     

                                                (1/2)
              /                               2\    
              |    /1    /175 \   1    /-175\\ |    
        + 700 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /     

                                               (1/2)
              /                              2\    
              |    /1    /175\   1    /-175\\ |    
        + 700 |1 + |- exp|---| - - exp|----|| |    
              \    \2    \499/   2    \499 // /     

                                                (1/2)     
              /                               2\          
              |    /1    /-350\   1    /350 \\ |          
        + 350 |1 + |- exp|----| - - exp|----|| |      + 350
              \    \2    \1497/   2    \1497// /           

                                                (1/2)
              /                               2\    
              |    /1    /350 \   1    /-350\\ |    
        + 350 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /     

                                                (1/2)
              /                               2\    
              |    /1    /700 \   1    /-700\\ |    
        + 175 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /    
                          4354.742601
> L := (1/3)*h*(y(x[1])+4*add(y(i), i = y(x[2]) .. y(x[N]), 2)+2*add(y(i), i = y(x[3]) .. y(x[N-1]), 2)+y(x[N+1])); evalf(L);
Error, invalid input: add expects 2 arguments, but received 3
                          4354.742601

I am trying to compare time taken in minutes for each iterative model(Jacobi, Gauss-Seidel and SOR) to complete, so as to figure out the iterativre model with a faster time of convergence but i don't know the command to initiate.

Anyone can help me to convert the following maple solution expressed by the hypergeom function to the LegendreP(n,b,x) or Q function?


 

restart

with(PDETools):

infolevel[pdsolve] := 3:

sol[1] := dsolve((1-x^2)*(diff(y(x), x, x))+n(n+1)*y(x) = 0)

y(x) = _C1*(-1+x^2)*hypergeom([3/4+(1/4)*(4*n(n+1)+1)^(1/2), 3/4-(1/4)*(4*n(n+1)+1)^(1/2)], [1/2], x^2)+_C2*(x^3-x)*hypergeom([5/4+(1/4)*(4*n(n+1)+1)^(1/2), 5/4-(1/4)*(4*n(n+1)+1)^(1/2)], [3/2], x^2)

(1)

convert(sol[1], LegendreP)

y(x) = _C1*(-1+x^2)*hypergeom([3/4+(1/4)*(4*n(n+1)+1)^(1/2), 3/4-(1/4)*(4*n(n+1)+1)^(1/2)], [1/2], x^2)+_C2*(x^3-x)*hypergeom([5/4+(1/4)*(4*n(n+1)+1)^(1/2), 5/4-(1/4)*(4*n(n+1)+1)^(1/2)], [3/2], x^2)

(2)

``

 

Download convert-Legendre.mw

 

https://math.stackexchange.com/questions/3254765/how-to-convert-a-hypergeom-function-to-the-legendre-function

I just want y(x) to be expressed in the form of LegendreP(n,b,x).

i have a assignment problem to optimize with 1200 variables and almost 1000 constraints. but maple couldnt solve it. anyone who can help me is welcome

or may i try another app?

thanks

this is the my model
tam2.mw

 

restart;

 

 

we:=[1,2,8,9,15,16,22,23,29,30];

(1)

wd:=[3,4,5,6,7,10,11,12,13,14,17,18,19,20,21,24,25,26,27,28];

(2)

#printlevel :=3;

for j from 1 to 30 do
#her gündüz vardiyasında en az 4 hemşire bulunsun
a[j]:=sum(x[i][j][1], i=1..20)>=4:
end do;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(3)

A := [seq(a[j],j=1..30)];

(4)

#her gece vardiyasında en az 4 hemşire bulunsun
for j from 1 to 30 do
b[j]:=sum(x[i][j][2], i=1..20)>=4:
end do;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(5)

 

B := [seq(b[j],j=1..30)];

(6)

#her hemşire ayda en az 4 hafta içi gündüz vardiyasında çalışsın
for i from 1 to 20 do
c[i]:=sum(x[i][wd[k]][1], k=1..20)>=4:
end do;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(7)

C := [seq(c[i],i=1..20)];

(8)

#her hemşire ayda en az 4 hafta içi gece vardiyasında çalışsın
for i from 1 to 20 do
d[i]:=sum(x[i][wd[k]][2], k=1..20)>=4:
end do;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(9)

dd:= [seq(d[i],i=1..20)];

(10)

#her hemşire ayda en az 2 hafta sonu gündüz vardiyasında çalışsın
for i from 1 to 20 do
e[i]:=sum(x[i][we[k]][1], k=1..10)>=2;
end do;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(11)

E:= [seq(e[i],i=1..20)];

(12)

#her hemşire ayda en az 2 hafta sonu gece vardiyasında çalışsın
for i from 1 to 20 do
f[i]:=sum(x[i][we[k]][2], k=1..10)>=2;
end do;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(13)

F:= [seq(f[i],i=1..20)];

(14)

#gece vardiyasında çalışan hemşire ertesi gündüz ve gece vardiyalarında izinlidir
for i from 1 to 20 do
for j from 1 to 29 do
g[i][j]:=2*x[i][j][2]+x[i][j+1][1]+x[i][j+1][2]<=2
end do;
end do;

for i from 1 to 20 do
g[i] := seq(g[i][j],j=1..29)
end do;

g:= [seq(g[i],i=1..20)];

with(Optimization);

Minimize( sum(t[m], m=1..20),{A[],B[],C[],dd[],E[],F[],g[]}, assume = binary );


 

Download tam2.mw

 

I need help on solving the following PDE by Maple:

https://math.stackexchange.com/questions/3177491/how-to-solve-the-given-partial-differential-equation

I couldn't write the partial differential equation in Mapleprimes so provided the link from somewhere else. Please help. Thank you.

Hi guys,

This is the first time of solving partial differential equation, can some please help me point out some errows in my code. 
 

restart

ODEs := `<,>`(diff(v(y), y, y)+(diff(v(y), y))/y-(Ha^2/(1-eta)^2+1/y^2)*v(y)-Re*v(y)*(diff(v(y), y)) = 0, diff(theta(y), y, y)+Ec*Pr*(diff(v(y), y)-v(y)/y)^2-Pr*Re*v(y)*(diff(theta(y), y))+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0, diff(phi(y), y, y)-Re*Sc*v(y)*(diff(phi(y), y))+Nt*(diff(theta(y), y, y)+(diff(theta(y), y))/y)/Nb = 0)

ODEs := Matrix(3, 1, {(1, 1) = diff(diff(v(y), y), y)+(diff(v(y), y))/y-(Ha^2/(1-eta)^2+1/y^2)*v(y)-Re*v(y)*(diff(v(y), y)) = 0, (2, 1) = diff(diff(theta(y), y), y)+Ec*Pr*(diff(v(y), y)-v(y)/y)^2-Pr*Re*v(y)*(diff(theta(y), y))+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0, (3, 1) = diff(diff(phi(y), y), y)-Re*Sc*v(y)*(diff(phi(y), y))+Nt*(diff(diff(theta(y), y), y)+(diff(theta(y), y))/y)/Nb = 0})

(1)

BCs := `<,>`(phi(eta) = 1, v(eta) = 1, theta(eta) = 1, phi(1) = 0, theta(1) = 0, v(1) = 0)

BCs := Matrix(6, 1, {(1, 1) = phi(eta) = 1, (2, 1) = v(eta) = 1, (3, 1) = theta(eta) = 1, (4, 1) = phi(1) = 0, (5, 1) = theta(1) = 0, (6, 1) = v(1) = 0})

(2)

param_names := [eta, Ha, Ec, Nt, Nb, Re, Sc, Pr];

[eta, Ha, Ec, Nt, Nb, Re, Sc, Pr]

(3)

pdSolve := subs(_P = param_names, proc ({ eta::realcons := .5, Ha::realcons := 1, Sc::realcons := .8, Nt::realcons := .1, Nb::realcons := .1, Re::realcons := 2, Ec::realcons := 0.1e-1, Pr::realcons := 10 }) userinfo(1, Solve, `~`[`=`](param_names, _P)); dsolve(eval(`union`(convert(ODEs, set), convert(BCs, set)), `~`[`=`](param_names, _P)), numeric) end proc);

proc ({ Ec::realcons := 0.1e-1, Ha::realcons := 1, Nb::realcons := .1, Nt::realcons := .1, Pr::realcons := 10, Re::realcons := 2, Sc::realcons := .8, eta::realcons := .5 }) userinfo(1, Solve, `~`[`=`](param_names, [eta, Ha, Ec, Nt, Nb, Re, Sc, Pr])); dsolve(eval(`union`(convert(ODEs, set), convert(BCs, set)), `~`[`=`](param_names, [eta, Ha, Ec, Nt, Nb, Re, Sc, Pr])), numeric) end proc

(4)

infolevel[Solve] := 1:

Fig. 3 (changing values of Ha):

P:= Ha:
vals:= [1, 5, 10, 20]:
sols:= [seq(Solve(P= v), v= vals)]:
colors:= [red, green, blue]:
for F in [v,theta,phi](y) do
   print(plots:-display(
      [seq(
         plots:-odeplot(sols[k], [y,F], color= colors[k], legend= [P= vals[k]]),
         k= 1..nops(vals)
      )],
      labeldirections= [horizontal,vertical]
   ))
od:

Error, pdeplot is not a command in the plots package

 

``


 

Download chapter5.mw

 

i have a problem to solve this system ?

Hello,

I will explain my problem on a simple function and some data.

mg:=78.54*7.85*1e-9*1000*9.81;l:=10000;l0:=12000;h:=0;H := 28.399;
eta:=mg*l/(2*H);
zeta:=arcsinh(mg*h/(2*H*sinh(eta)))-eta;
z:=H/mg*(cosh(mg/H*x+zeta)-cosh(zeta));
plot(z,x=0..l);

Above is a definition of an initial plot. Now I would like to draw a new plot in which every x coordinate is shifted horizontally by a function:

deltax:=H*arcsinh(x)-x;

As you see I can't use translate or scale so I've tried to use a transform function but I can't do it the right way.

I would be grateful for any ideas.

 

Greetings,

Iza

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