MaplePrimes Questions

Hi,

I am trying to solve a set of homogeneous equations for the non-trivial solutions. Mathematically it is possible to get it. But is there any way to get it in Maple. Please find the attached maple sheet for the question. Please help me regarding this.

Regards

Sunit

restart

with(plots):

with(LinearAlgebra):

eq[1] := diff(x[1](t), t)-x[2](t)

diff(x[1](t), t)-x[2](t)

(1)

eq[2] := diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

(2)

eq[3] := diff(phi[1](t), t)-phi[2](t)

diff(phi[1](t), t)-phi[2](t)

(3)

eq[4] := diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

(4)

for k to 4 do eqn[k] := simplify(coeff(map(expand, eval(eq[k], [x[1] = (proc (t) options operator, arrow; x[1]*exp(lambda*t) end proc), x[2] = (proc (t) options operator, arrow; x[2]*exp(lambda*t) end proc), phi[1] = (proc (t) options operator, arrow; phi[1]*exp(lambda*t) end proc), phi[2] = (proc (t) options operator, arrow; phi[2]*exp(lambda*t) end proc)])), exp(lambda*t))) end do

x[1]*lambda-x[2]

 

x[2]*lambda+2*zeta*beta*x[2]+beta^2*x[1]-n*psi*v*phi[1]+n*psi*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*psi*x[1]-n*psi*x[1]*exp(-2*lambda*Pi/(n*omega0))

 

phi[1]*lambda-phi[2]

 

phi[2]*lambda+2*kappa*phi[2]+phi[1]-n*v*phi[1]+n*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*x[1]-n*x[1]*exp(-2*lambda*Pi/(n*omega0))

(5)

A, b := GenerateMatrix([seq(eqn[k], k = 1 .. 4)], [x[1], x[2], phi[1], phi[2]])

A, b := Matrix(4, 4, {(1, 1) = lambda, (1, 2) = -1, (1, 3) = 0, (1, 4) = 0, (2, 1) = beta^2+n*psi-n*psi*exp(-2*lambda*Pi/(n*omega0)), (2, 2) = 2*Zeta*beta+lambda, (2, 3) = n*psi*v*exp(-2*lambda*Pi/(n*omega0))-n*psi*v, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = lambda, (3, 4) = -1, (4, 1) = n-n*exp(-2*lambda*Pi/(n*omega0)), (4, 2) = 0, (4, 3) = -n*v+1+n*v*exp(-2*lambda*Pi/(n*omega0)), (4, 4) = 2*kappa+lambda}), Vector(4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0})

(6)

right_vector := Matrix(4, 1, [r[1], r[2], r[3], r[4]])

right_vector := Matrix(4, 1, {(1, 1) = r[1], (2, 1) = r[2], (3, 1) = r[3], (4, 1) = r[4]})

(7)

junk := MatrixVectorMultiply(subs(lambda = I*omega, A), right_vector)

junk := Matrix(4, 1, {(1, 1) = I*omega*r[1]-r[2], (2, 1) = (beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*Zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3], (3, 1) = I*omega*r[3]-r[4], (4, 1) = (n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(-n*v+1+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]})

(8)

junk(1)

I*omega*r[1]-r[2]

(9)

for k to 4 do eqnn[k] := junk(k) end do

I*omega*r[1]-r[2]

 

(beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3]

 

I*omega*r[3]-r[4]

 

(n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(1-n*v+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]

(10)

solve({seq(eqnn[k], k = 1 .. 4)}, {seq(r[k], k = 1 .. 4)})

{r[1] = 0, r[2] = 0, r[3] = 0, r[4] = 0}

(11)

``

``

``

 

Download question4.mw

Hello all..

Im sharena and i am solving ODE BVP by using maple. i used this command to solved the equation..

 

However, i dont know which method this programm solved my ODE. Is it RK45 method??

Hello Everyone,

May I ask you about this  "Error,   (in pdsolve/numeric/process_PDEs)  number of dependent variables and number of PDE must be the same". Does anyone have idea about solving linear instability equation (flow inside pipe, oscillating flow) ?

Thank you,

 

 

 

Hello, I need help in add/sum, there are two problems:

 

1. How we write triple summation (sigma) in Maple? (See pic)

Pic 1 (Triple Sigma)

I try sum(sum(sum or add(add(add but it isn't working.

 

 

2. How we write summation like in this pic?

Pic 2

I already try these syntax:

for e from 1 to 9 do

for k from 1 to 17 do

if i=(2*e-1) then next else

constraint12[2*e-1,k]:=add(x[2*e-1,i,k],i from i in T)=1

end if

end do

end do

 

For example, the expected result for e=2 and k=1 is like following equation:

x[2,1,1]+x[2,3,1]+x[2,4,1]+x[2,5,1]+...+x[2,17,1]+x[2,18,1]=1

But the result I get:

x[2,1,1]+x[2,2,1]+x[2,3,1]+...+x[2,18,1]=1

 

How to omit the x[2,2,1]?

 

Thank you.

pls help review this code, its doesnt return a solution

 

 

restart;
Digits := 16;
M := .5; lambda := .5; Pr := .72; beta := 1; L[w] := 0; m := 1; R := 1; Ec := 1;
N := 7;
for j from 0 to N do J[j] := sum(f[k](t)*(diff(f[j-k](t), `$`(t, 2))), k = 0 .. j) end do;
for i from 0 to N do K[i] := sum((diff(f[k](t), t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
for j from 0 to N do G[j] := sum(f[k](t)*(diff(theta[j-k](t), t)), k = 0 .. j) end do;
for j from 0 to N do H[j] := sum((diff(f[k](t), t))*theta[j-k](t), k = 0 .. j) end do;
for i from 0 to N do P[i] := sum((diff(f[k](t), t, t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
epsilon := 1; delta := 0;
f[0] := proc (t) options operator, arrow; L[w]+epsilon+delta*A*t+(1/2)*A*t^2 end proc;
1 2
t -> L[w] + epsilon + delta A t + - A t
2
theta[0] := proc (t) options operator, arrow; 1+B*t end proc;
t -> 1 + B t
NULL;
;
NULL;
NULL;
NULL;
NULL;
for i to N do f[i] := simplify(-((m+1)*(1/2))*(int(int(int(J[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))+m*(int(int(int(1-K[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-M*(int(int(int(diff(f[i-1](t), t)-1, t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-lambda*(int(int(int(theta[i-1](t), t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))); f[i] := unapply(f[i], eta); theta[i] := simplify(-3*Pr*R*(((m+1)*(1/2))*(int(int(G[i-1], t = 0 .. eta), t = 0 .. eta))-(2*m-1)*(int(int(H[i-1], t = 0 .. eta), t = 0 .. eta))+Ec*(int(int(P[i-1], t = 0 .. eta), t = 0 .. eta)))/(4+3*R)); theta[i] := unapply(theta[i], eta) end do;
NULL;
F(eta):=collect((∑)f[z](eta),eta):
Theta(eta):=collect((∑)theta[z](eta),eta):
with(numapprox);
for k from 2 to 5 do W[k] := pade(diff(F(eta), eta), eta, [k, k]); Q[k] := pade(Theta(eta), eta, [k, k]); SOLL1[k] := expand(coeff(numer(W[k]), eta^k)) = 1; SOLL2[k] := expand(coeff(numer(Q[k]), eta^k)) = 0; SOL[k] := solve({SOLL1[k], SOLL2[k]}, {A, B}); print([k] = SOL[k]) end do;
Warning, computation interrupted

 

 

 

 

 

 

Hello

It has been years since I last used maple so I apologize if my question makes no sense and my code is outdated (and wrong!).   

I need to write a function (proc) that uses a functional operator inside.  Something like

test:=proc()

local f,vars, func, aux, res;

f:=arg[1]; # a list

vars:=arg[2]: # a list

aux:=op(vars):

func:=aux -> f:  # a function from () to []

res:=func(op(func(aux))):

return(res):

end:

 

This is the basic idea of the proc.  If f:=[y, y*z-x, -15*x*y-x*z-x] and vars:=[x,y,z], the function of a function does not return as it supposes to.  Please tell me what I am doing wrong and how to improve and update the code.

 

many thanks

 

Ed

 

 

 

im just getting a generic recursive assignment plus first unused arg error

thats what the maple engine says im doing wrong ill get the number of recursives counted but i guess it just makes me the most angry because its like the same type of error for me every ******* time

hy 
need help 
i made this code but i can not get the answer ,help me to find out where i did wrong.

thanx in advance




restart;
f:=x->(x^3+3*x^2-1);
n:=30;
tol:=1e-9;
a[0]:=0;
b[0]:=10;
Digits :=15;

 

printf("No root F(x) abs(x[i+1]-x[i])\n");

for i from 1 to n do
t[i-1] :=evalf( (b[i-1]-a[i-1])/(f(b[i-1])-f(a[i-1])));
c[i-1] := evalf((a[i-1]*f(b[i-1])-b[i-1]*f(a[i-1]))/(f(b[i-1])-f(a[i-1])));
x[i] :=evalf( x[i-1]-t[i-1]*f(x[i-1])^2/(f(x[i-1])-f(c[i-1])));

printf("%d %10.15f %10.15f %10.15e \n",i,x[i],f(x[i]),abs(x[i]-x[i-1]));
if f(a[i-1])*f(c[i-1])<0 then
a[i]:=a[i-1];
b[i]:=c[i-1];
else
a[i]:=c[i-1];
b[i]:=b[i-1];
if abs(f(x[i]))<tol then
print("approximate solution"= x[i]);
print("No of iterations"= i);
break;
end if;
end if;
end do:

Hey 

 

I just went from maple 18 to maple 2016. I use maple as a writing program aswell for notes and school.

 

I realized that maple 2016 does output lines when writing math in a textbox. This is kind of annoying since notes in chemistry is not allways a true mathematical expression. Therefore maple complains. Is there anyway to change this? 

Andreas

Hi all,

I was wondering how to go about validating some airfoil designs for my Formula SAE team's CFD results.  I know this is more common with simplier calculations but I'm hoping using Maple and maybe the new algebraic manipulation of non-comunitive differential operators, I could achive what I am after.   The two calculations of interest are the drag force and downforce.  Can someone shed some light? Thanks

Lets say we have to vectors u := Vector(3,[0,a_2,a_3]) and v :=Vector(3,[a_1,a_2,a_3]), in which a_1, a_2 and a_3 are arbitrary constants. It is clear that if we set a_1=0 we could see that u is contained in the vector space of v. Is there a function in Maple like isSubspace(u,v) which returns a boolean true or false?

An alternative interpretation could be that the image of u is a subset of the image of v.

Thank you alot for reading my question. 

 

When I try to use CodeTools:-Profiling:-Profile() (with no arguments), I get "kernel connection lost" after about a minute. Has anyone used this sucessfully, with no arguments? If so, would you please post a worksheet? I'm using Windows 8, if that makes a difference.

I think that I'll need to revert to the older kernelopts(profile= true).

In Maple V, Release 4 (1996):

 

_EnvX:=0; b:=0; proc() global b; print(_EnvX, b); assign('_EnvX=1, b=1'); print(_EnvX, b); end();
_EnvX:=0: b:=0: proc() global b; print(_EnvX, b); _EnvX:=1; b:=1; print(_EnvX, b); end();;

gives:
                                 0, 0
                                 0, 1

In newer Maple:

 

_EnvX:=0; b:=0; proc() global b; print(_EnvX, b); assign('_EnvX=1, b=1'); print(_EnvX, b); end proc();
_EnvX:=0: b:=0: proc() global b; print(_EnvX, b); _EnvX:=1; b:=1; print(_EnvX, b); end proc();

?


Hello! 

I'm trying to plt something, I can't see why Maple isn't multiplying these two rows as it should. 

Can anyone see the problem?

 

This preamble is loaded:

restart;

with(Units[Standard]);
with(ArrayTools);

with(LinearAlgebra);

with(Statistics);
with(plots);
with(CurveFitting);

 

 

 

 

 

with(plots):

with(LinearAlgebra):

 

asd := [3.5400000*10^5, 3.4700000*10^5, 3.3700000*10^5, 3.2700000*10^5, 3.1700000*10^5, 3.0900000*10^5, 3.0300000*10^5, 2.9600000*10^5, 2.9200000*10^5, 2.8900000*10^5, 2.8600000*10^5, 2.8500000*10^5, 2.8200000*10^5, 2.8100000*10^5, 2.7900000*10^5, 2.7800000*10^5, 2.7800000*10^5, 2.7700000*10^5, 2.7600000*10^5]:
 

NULL

asf := [0.2866400798e-1, 0.6112772793e-1, 0.9946549241e-1, .1349950150, .1645923341, .1877395591, .2054364684, .2189514789, .2293646837, .2374847679, .2439099369, .2490583805, .2532402792, .2566744211, .2595269747, .2619197962, .2639470478, .2656751966, .2671596322]:

 

asd*asf;

[354000.0000, 347000.0000, 337000.0000, 327000.0000, 317000.0000, 309000.0000, 303000.0000, 296000.0000, 292000.0000, 289000.0000, 286000.0000, 285000.0000, 282000.0000, 281000.0000, 279000.0000, 278000.0000, 278000.0000, 277000.0000, 276000.0000]*[0.2866400798e-1, 0.6112772793e-1, 0.9946549241e-1, .1349950150, .1645923341, .1877395591, .2054364684, .2189514789, .2293646837, .2374847679, .2439099369, .2490583805, .2532402792, .2566744211, .2595269747, .2619197962, .2639470478, .2656751966, .2671596322]

(1)

 

NULL

 

Thank you!

Download maple_what.mw

First 1085 1086 1087 1088 1089 1090 1091 Last Page 1087 of 2434