3d plot of a wave equation solution

Hi everybody,

after solving it a wave equation with separation of variables

I find the solution

with :

and i want to have a 3 d graph for for example for u(x,y,1,1) but I find it very difficult to do it.

i did this but it doesn't work:

clear all;close all;clc;

x=[0:.1:5];y=[0:.1:5];

[X,Y] = meshgrid(x,y);

for n=1:20

for m=1:20

for k=1:20

fun = @(a) sin((n*pi/5)*a);

fun2 = @(c) sin((m*pi/5)*c)*integral(fun,0,5);

fun3 = @(c) sin(k*c)*integral(fun,0,5);

Z1(n,m,k)=(8/(3*(10^8)*5*5*sqrt(1+((m*pi)/5)^2+((n*pi)/5)^2)))*...

integral(fun3,0,10)*sin(3*(10^8)*sqrt(k^2+(m*pi/5)^2+(n*pi/5)^2))*...

(sin((n*pi/5).*X)*sin((m*pi/5).*Y)*sin(k));

end

end

end

for n=1:20

for m=1:20

for m=1:20

Z=Z+Z1(n,m,k);

end

end

end

mesh(X,Y,Z)

please if anyone can help me

[darova]

You have in the second expression. It has no result. Am i wrong?

[Youssef FAKHREDDINE]

i think i must switch the infinty by a number λ for example which is big enough .

or bigger enought than 5 because i'm studing this wave in a rectangular wave guide a waveguide that is section and which is of great depth like a tunel.

Answer 1

[darova]

I used formula to generate x,y,z (t=1) and u0 = u(x,y,z,1) as color? Calculation takes some time. How to vectorize it?

That is what i got