Message Boards Message Boards

0
|
13037 Views
|
6 Replies
|
1 Total Likes
View groups...
Share
Share this post:

How to solve a PDE on Mathematica

Posted 8 years ago

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

Attachments:
POSTED BY: Pamela Vilela
6 Replies
Posted 8 years ago

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

POSTED BY: Bailey Kosky
Posted 8 years ago

Thanks a lot! :)

POSTED BY: Pamela Vilela

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}]
POSTED BY: Gianluca Gorni
Posted 8 years ago

Many thanks! I'll give it a try now!

POSTED BY: Pamela Vilela
Posted 8 years ago
POSTED BY: Pamela Vilela

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}]
POSTED BY: Gianluca Gorni
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract