Hello everyone! so I want to know how to plot/(get the answer also) to this Second order partial differential equation on wolfram alpha, or actually any program that can do it online. so it goes like this:
Solve: Uxx + Uyy = 0 for 0 < x < L and 0 < y < L
At x = 0, U = 0
At y = 0, U = 0
At x = L, U = 0
At y = L, U = f(x)
being Uxx = d^2u/dx^2 and Uyy=d^2u/dy^2
MANYYYY MANY thanks
laplaceequation=d^2u[x,y]/dx^2+d^2u[x,y]/dy^2==0;
boundaryconditions={u[0,y]==0,u[L,y]==0,u[x,0]==0,u[x,y]==0};
dsol= DSolve[{laplaceequation,boundaryconditions},u,{x,y}]
And it didn't work :/
How are you writing your boundary conditions?
There are limits to how much you can expect out of Wolfram|Alpha. Some things, like this, you need to use Mathematica Online for.
https://www.wolfram.com/mathematica/online/
See this recent blog post here. The author covers how to solve Laplace's equation for different kinds of boundary conditions symbolically and what it is capable of doing on it's own symbolically:
http://blog.wolfram.com/2016/01/07/new-in-the-wolfram-language-symbolic-pdes/
Note that it's not going to show you the steps it took to solve the equation. This is well beyond that level of math.
Thank you so much! I'll give it a look right now! :)
Dear Sean,
I had a go with Mathematica, but I had to buy it first so I've paid like 60+£ now hahaha I also had a look to that PDE blog post, and yet haven't been able to solve it, I believe that since it is my first time using this language I can't do it right, are you able to show how to do the input so I can copy paste it and see how it works? Many thanks.
