I try to get real solutions for a PDE, i.e. real-valued functions depending on real variables. Maple computer complex solutions, i.e. complex-valued functions depending on complex variables.

Here is the example in question: (the four function f1, f2, f3, f4 depend on the four unknowns lam, mu, l, m)

`assuming`([pdsolve([diff(f2(lam, mu, l, m), m)-(diff(f1(lam, mu, l, m), l))-(diff(f4(lam, mu, l, m), mu))+diff(f3(lam, mu, l, m), lam) = 0, diff(f1(lam, mu, l, m), m)+diff(f2(lam, mu, l, m), l)-(diff(f3(lam, mu, l, m), mu))-(diff(f4(lam, mu, l, m), lam)) = 0])], [real])

How can I solve my problem and receive only real solutions to my PDE?

A similar problem had been posted before (see here), but I can only find a cached version of the post where no answers are displayed.

Dear Users!

Hope you would be fine. In the following maple code, I want to write the derivative of psi in term of psi like it did manually in red portion. For higher M and k it very hard to do it manully. It there any command to fix my problem for any value of k and M.

restart; k := 2; M := 4;

with(linalg); with(LinearAlgebra);

printlevel := 2;

for i while i <= 2^(k-1) do

for j from 0 while j <= M-1 do

psi[M*i+j-M+1] := simplify(2^((1/2)*k)*sqrt(GAMMA(j+1)*(j+alpha)*GAMMA(alpha)^2/(Pi*2^(1-2*alpha)*GAMMA(j+2*alpha)))*(sum((-1)^i1*GAMMA(j-i1+alpha)*(2*(2^k*x-2*i1+1))^(j-2*i1)/(GAMMA(alpha)*factorial(i1)*factorial(j-2*i1)), i1 = 0 .. floor((1/2)*j))));

`&psi;&psi;`[M*i+j-M+1] := simplify(diff(psi[M*i+j-M+1], x))

end do

end do; r := 2^(k-1)*M;

VV := Vector[column](r, proc (i) options operator, arrow; psi[i] end proc);

DV := Vector[column](r, proc (i) options operator, arrow; `&psi;&psi;`[i] end proc);

``&psi;&psi;`[2] := 8*sqrt((alpha+1)*(1/2))*sqrt(2)*sqrt(alpha*GAMMA(alpha)^2*4^alpha/GAMMA(2*alpha))/sqrt(Pi) = 8*sqrt((alpha+1)*(1/2))*psi[1];

`&psi;&psi;`[3] := 16*sqrt((2+alpha)*(alpha+1)/(1+2*alpha))/sqrt(2)*(2*sqrt(2)*sqrt((alpha+1)*GAMMA(alpha)^2*4^alpha/GAMMA(1+2*alpha))*alpha*(4*x+1)/sqrt(Pi)) = 16*sqrt((2+alpha)*(alpha+1)/(1+2*alpha))*psi[2]/sqrt(2)

I am waiting your response. Thanks

Dear Users! 

Hope you would be fine with everything. I want to define a matrix F of M+1 by M+1 order having element of the following form:

I derived the F[r,s] but confuse who to generate matrix now.

restart; M := 5; printlevel := 3; for r from 2 while r <= M+1 do for s while s <= r-1 do if type(r+s, odd) then F[r, s] := 2^(k+1)*sqrt((2*r-1)*(2*s-1)) end if end do end do

Dear Users!

Hoped everyone fine with everything. I the following maple expression, I need a matrix A for each n. Like if I take k =1 I want A[1]; if I take k=2, I want A[1], A[2]; for k=3 I want A[1], A[2], A[3] and so on. A[i]'s is square matrix having order M-1 by M-1.

Further I want to generate a block matrix for k. Like for k=1 I want a block matrix as Vector(1, {(1) = A[1]}), for k=2 I want a block matrix as Matrix(2, 2, {(1, 1) = A[1], (1, 2) = 0, (2, 1) = 0, (2, 2) = A[2]}), for k =3 I want a block matrix as Matrix(3, 3, {(1, 1) = A[1], (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = A[2], (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = A[3]}) and so on.

restart; alpha := 1;
k := 2; M := 3;
printlevel := 3;

for n while n <= 2^(k-1) do

for m from 0 while m <= M-1 do

for j from 0 while j <= M-1 do

Omega[m, j] := 2^((1/2)*k)*sqrt(GAMMA(j+1)*(j+alpha)*GAMMA(alpha)^2/(Pi*2^(1-2*alpha)*GAMMA(j+2*alpha)))*(sum((-1)^i*GAMMA(j-i+alpha)*2^(j-2*i)*(sum((1/2)*binomial(m, l)*(2*n-1)^(m-l)*(1+(-1)^(j-2*i+l))*GAMMA((1/2)*j-i+(1/2)*l+1/2)*GAMMA(alpha+1/2)/GAMMA(alpha+1+(1/2)*j-i+(1/2)*l), l = 0 .. m))/(GAMMA(alpha)*factorial(i)*factorial(j-2*i)), i = 0 .. floor((1/2)*j)))/2^(k*(m+1))

end do

end do;

A[n]:=???

end do;

I am waiting for your positive response.

Thanks
 

Dear Users!

Hoped everyone is good. I am facing problem to write the following sigma notation for any m.

Please help me to fix this problem. Thanks

Say I have an expression

ex:=sqrt(x)/2h

what do I tell maple to pull the 2h into the sqrt

sqrt(x/4h^2)

Dear User!

Hoped you all are fine with everything. I am facing to determinte the integration of the following for n = 0 and for n>=1.

int(2*x^i*(x+n)^m*sqrt(-x^2+x), x = 0 .. 1)

Dear Users!

Hoped everyone fine with everything! I want to define a square matrix P whose elements are

p[i,j]=<φ[i],ψψ[j]>

printlevel := 2; for i from 0 while i <= 2^k-1 do for j from 0 while j <= M-1 do varphi[i, j] := t^j end do end do;
printlevel := 2; for i from 0 while i <= 2^k-1 do for j from 0 while j <= M-1 do phi[M*i+j+1] := varphi[i, j] end do end do;
printlevel := 2; for i from 0 while i <= 2^k-1 do for j from 0 while j <= M-1 do psi[i, j] := 2^((1/2)*k)*sqrt(2*j+1)*(sum((-1)^(j+i1)*factorial(j+i1)*(2*t-i)^i1/(factorial(j-i1)*factorial(i1)^2), i1 = 0 .. j)) end do end do;
printlevel := 2; for i from 0 while i <= 2^k-1 do for j from 0 while j <= M-1 do `&psi;&psi;`[M*i+j+1] := psi[i, j] end do end do;
 

take k=2,M=3

Hello Guys, I hope you are all fine. I have been struggling with creating an animation of the points (x,y) in maple. I have tried this example 
L := [[1, 1], [3, 2], [3.4, 6], [5, 3, 7], [3, 7, 9, 1], [2, 6, 8, 4, 5]];
animate(PointPlot, [L[trunc(t)]], t = 1 .. 6, frames = 150)
but in my case it shows two points at different location means it takes x and y seperate value and showed it on 1 and 2 on x axis but i want to animate it as the location of point. Please help me. 
Thank you in anticipation.

Help me about Tabulate and append text below.

file help: text_and_tabulate.mw

Dear Users!

Hope everyone is fine. I am want use the command of isolate only red color term. Then I need help to simplify the expression term by term like simplify the rational expressions, combine powers, simplify radicals etc..

x*c*(diff(f(eta), eta))*epsilon/(-epsilon*t+1)^2+(1/2)*x*c^2*(diff(f(eta), eta, eta))*y*epsilon/((-epsilon*t+1)^3*sqrt(c/(nu*(-epsilon*t+1)))*nu)+x*c^2*(diff(f(eta), eta))^2/(-epsilon*t+1)^2-sqrt(c*nu/(-epsilon*t+1))*f(eta)*x*c*(diff(f(eta), eta, eta))*sqrt(c/(nu*(-epsilon*t+1)))/(-epsilon*t+1) = a*x*epsilon/(-epsilon*t+1)^2+a^2*x/(-epsilon*t+1)^2+x*c^2*(diff(f(eta), eta, eta, eta))/(-epsilon*t+1)^2+sqrt(2)*GAMMA*x^2*c^3*(diff(f(eta), eta, eta))*sqrt(c/(nu*(-epsilon*t+1)))*(diff(f(eta), eta, eta, eta))/(-epsilon*t+1)^3+A*g*beta[T]*theta(eta)*T[w]-A*g*beta[T]*theta(eta)*T[infinity]+A*g*beta[C]*phi(eta)*C[w]-A*g*beta[C]*phi(eta)*C[infinity]-sigma*B^2*x*c*(diff(f(eta), eta))/(rho*(-epsilon*t+1))+sigma*B^2*a*x/(rho*(-epsilon*t+1))

I am waiting your postive answer on it.

please help me out with maple code/script for vander pol limit cycle using its differential equation..

How do I plot the following with Maple 2015?

Dear users!

Hope everyone should be fine. I have some query regarding to set title of the following problem in 2D

beta := 1; alpha[1] := .5

f := beta+alpha[1]+sin(x*beta);

plot(f, x = 0 .. Pi, axes = boxed, size = [300, 270], labels = [x, "f ' (x)"], labelfont = ["Arial", 10, Bold], labeldirections = [horizontal, vertical], title = "&beta; = 1, &alpha;[1] = 0.5\n", titlefont = ["Arial", 10, Bold]);

I got the following graph

but I need the following one

Want to shift title on right. Want to write alpha[1] and f like in figure 2. 

I am waiting your response. Thanks

Dear users! 

Hope everyone fine with everything. I want to chage the format of x-axis in the attached file. I need the x-axis in degree like (-180^o, -120^o, -60^o, 0 , 60^o, 120^o, 180^o). Also I want the lable on y-axis as:

I am waiting your positive respons. 

Help_new.mw