Hello everyone! so I want to know how to plot/(get the answer also) to this Second order partial differential equation on mathematica, I can't seem to get the input right
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
Just Go here this is Best answer for this question -
https://reference.wolfram.com/language/howto/SolveAPartialDifferentialEquation.html
Thanks , :)
Discover more architectural and #3D_Rendering inspirations on
http://www.thecheesyanimation.com
Thanks a lot! :)
This is very similar to an example in the documentation for DSolve > Examples > Scope > Elliptic Partial Differential Equations (with Mma 10.3.1):
leqn = {Laplacian[u[x, y], {x, y}] == 0}; bc = {u[0, y] == 0, u[x, 0] == 0, u[L, y] == 0, u[x, L] == f[x]}; DSolve[{leqn, bc}, u[x, y], {x, y}]
Many thanks! I'll give it a try now!
Hey, thanks very much for the code! it was extremely useful! I have now to input a very similar problem but the boundary conditions change and I'm kinda stuck there so I was wondering if I could ask you again! :) so now my new boundary conditions are:
At x = 0, dU/dx = 0
At x = a, dU/dx = 0
At y = b, U = f(x)
As you can figure, the problem is inserting the derivativs dU/dx in the boundary conditions I don't really know how to do that, please help!
To enter partial derivatives in non-generic points you can use the syntax Derivative[n1,n2][u]:
DSolve[{Laplacian[u[x, y], {x, y}] == 0, Derivative[1, 0][u][0, y] == 0, u[x, 0] == 0, Derivative[1, 0][u][a, y] == 0, u[x, b] == f[x]}, u[x, y], {x, y}]
