Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Numerical Solution of 4D PDE

  1. Apr 20, 2012 #1

    I want to solve a 4-dimensional PDE problem using some numerical code. Possibly MATLAB or Python.

    I have a solved a simple version of the PDE in 2D using MATLAB PDETool.
    Also I solved a simplified pde in 3D using FiPy library in Python.

    However, most MATLAB existing tools allow 2D problem solution, while FiPy allowed me to go upto 3D.

    I am looking for some help for a Finite Difference Method to solve following PDE.
    4 variables - x_1 to x_4

    In Latex Notation:

    [itex]\frac{\partial^2 u}{\partial x_3^2} + \frac{\partial^2 u}{\partial x_4^2} -
    x_3 \frac{\partial u}{\partial x_1} - x_4 \frac{\partial u}{\partial x_2} = 0 [/itex]

    Boundary Condition: (boundary is circles in x_1 - x_2 plane.)(x_3 x_4 in R plane)

    [itex]u = 0 \ \text{for} \ x_1^2 + x_2^2 = 1 \ \text{and} \ (x_1 x_3 + x_2 x_4) \geq 0 [/itex]
    [itex]u = 1 \ \text{for} \ x_1^2 + x_2^2 = 0.1 \ \text{and} \ (x_1 x_3 + x_2 x_4) < 0 [/itex]

    Appreciate any help and comments.

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted