Plotting the solution to the Laplace equation

Hi guys, I am trying to plot the solution to a PDE. I was given the laplace equation where u(x,y) is

L= pi, and H= pi/4. I want to plot the solution in 2D. This is what I have so far.

for c = 1:10
g = sin(pi.*c);
for n=1: 10
    L = pi;
    H= L/4;
    for x = 0:L
        integral = g*sin((n.*pi.*x)/L);
    end
    an = 2/(n.*pi*sinh((n.*pi*H)/2)).*integral;
    uxy = an*sin((n.*pi.*c)/L)*cosh(n.*pi*(y-H)/2);
end
end
figure;
plot(x,uxy)

When I run it, it gives me a blank plot. Any tips on how to fix this or fix some of my coding errors? It would be much appreciated!

[A. Sawas]

You are not keeping the interim results in the two loops you have in the code. Eventually, (x, uxy) is a single point.

Try this to see this point:

plot(x,uxy, '+');

Answer 1

[Agnish Dutta]

I suggest using the symbolic mathematics toolbox which provides functions for solving, plotting, and manipulating symbolic math equations.

"u(x, y)" seems like a bivariate function. To plot such a function, have a look at the "Generate surfaces z=f(x,y) without meshgrid" section of the following document:

https://www.mathworks.com/help/symbolic/examples/analytical-plotting-with-symbolic-math-toolbox.html#AnalyticalPlotingWithSymbolicMathToolbox-10

You will find multiple other tools for plotting functions of different types in the above page.

Also, please have a look at the following MATLAB answers page containing a similar problem:

https://www.mathworks.com/matlabcentral/answers/402428-how-can-i-plot-this-solution-to-laplace-s-equation?s_tid=answers_rc1-1_p1_BOTH