Constructing a Contour Plot for Solving a PDE with a Summation Formula

[Dustinsfl]

$$
u(x,y) = \frac{4}{\pi}\sum_{n = 1}^{\infty}\left[\frac{\sin(2n - 1)\pi x\sinh\left[(2n - 1)\pi (1 - y)\right]}{(2n - 1)\sinh(2n - 1)\pi} + \frac{\sin(2n - 1)\pi y\sinh\left[(2n - 1)\pi(1 - x)\right]}{(2n - 1)\sinh(2n - 1)\pi}\right].
$$

How do I construct a contour plot of this?

 

[Dustinsfl]

http://pauli.uni-muenster.de/tp/fileadmin/lehre/NumMethoden/WS0910/ScriptPDE/Heat.pdf

I would like to construct a plot like the one on page 9 fig 7.6 for my PDE. How can I do that?

 

[Dustinsfl]

>> [x,y]=meshgrid(-10:0.1:10, -10:0.1:10);
>> syms n;
>> z=symsum(4/pi*(sin((2*n-1)*pi*x)*sinh((2*n-1)*pi*(1-y))/((2*n-1)*sinh((2*n-1)*pi))+sin((2*n-1)*pi*y)*sinh((2*n-1)*pi*(1-x))/((2*n-1)*sinh((2*n-1)*pi))),0,20);
contour3(x,y,z)

I just tried this code but Matlab froze.

Any thoughts or suggestions?

 

[Sudharaka]

>> [x,y]=meshgrid(-10:0.1:10, -10:0.1:10);
>> syms n;
>> z=symsum(4/pi*(sin((2*n-1)*pi*x)*sinh((2*n-1)*pi*(1-y))/((2*n-1)*sinh((2*n-1)*pi))+sin((2*n-1)*pi*y)*sinh((2*n-1)*pi*(1-x))/((2*n-1)*sinh((2*n-1)*pi))),0,20);
contour3(x,y,z)

I just tried this code but Matlab froze.

Any thoughts or suggestions?

I tried this using Maxima. The code I used and the plots are given below.

expr:sum(4/%pi*(sin((2*n-1)*%pi*x)*sinh((2*n-1)*%pi*(1-y))/((2*n-1)*sinh((2*n-1)*%pi))+sin((2*n-1)*%pi*y)*sinh((2*n-1)*%pi*(1-x))/((2*n-1)*sinh((2*n-1)*%pi))),n,0,20)$

plot3d(expr, [x,-10,10],[y,-10,10],[grid, 150, 150]);

contour_plot(expr,[x,-15,15],[y,-10,10],[grid, 300, 300]);

3D Plot

Contour Plot

 

[Dustinsfl]

Is there anyway to plot the vector field of this?

 

[Sudharaka]

Is there anyway to plot the vector field of this?

To draw a vector field you need a vector valued function. But \(u\) is not a vector valued function.