plotting heat diffusion in a sphere

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dustin
dustin 2013-10-4
编辑： dustin 2013-10-11
I am trying to plot heat diffusion in a sphere but I am having no luck. I am trying to adapt my code for a square.
My code for a square is:
% Initialize square grid
[x, y] = meshgrid(0:0.005:1, 0:0.005:1);
nmax = 110;
T = zeros(length(x), length(y));
for n = 1:nmax
m = 2*n - 1;
T = T + 400/pi*sinh(m*pi*y)/(m*sinh(m*pi)).*sin(m*pi*x);
end
surface(x, y, T)
shading('interp')
colorbar
colormap jet
For the sphere, I have written (which doesn't work):
[x, y] = meshgrid(-1:.01:1, -1:.01:1);
[theta, r] = cart2pol(x, y);
N = 3;
p = zeros(length(N));
T = zeros(length(x), length(y));
fun = @(x) legendre(0, x);
for l = 0:N
p = p + 50*(2*l + 1).*integral(fun, 0, 1);
end
for n = 1:N
T = T + p.*r.^n.*legendre(0, cos(theta));
end
surface(theta, r, T) shading('interp') colorbar colormap jet
The Legendre integral isn't returning the correct coefficients. The first 3 are 50, 75, 0. The code is returning 50, 200, 450.
What is going wrong?

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