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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.

Thanks.

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# Numerical Solution of 4D PDE

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