# Plotting the solution to the Laplace equation

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Briyahna Deleon on 7 Apr 2019
Answered: Agnish Dutta on 11 Apr 2019
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!

#### 1 Comment

A. Sawas on 7 Apr 2019
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, '+');

Agnish Dutta on 11 Apr 2019
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:
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: