How do you analytically solve PDE's in Matlab for example the 1-D Poisson Equation

Hi there,

I'm reletively new to matlab and am wondering whether/how I can solve PDE's analytically. For example ∂²Φ/∂x² = 1. I would appreciate any advice/ what commands or rules I can use to do this. I very much appreciate any help anyone could provide in this matter.

Kindest Regards,

A

Answer 1

[Torsten]

Usually, PDEs cannot be solved analytically in MATLAB.

Your "PDE" is a simple ODE with solution phi(x) = 1/2*x^2 + a*x + b with free constants a and b:

syms x
d2phidx2 = sym('1');
phi = int(int(d2phidx2,x),x)

phi = 

For PDEs in one spatial dimension, MATLAB's "pdepe" is a numerical solver that can be used for PDEs of convection-diffusion-reaction type (not convection alone !)

[Alex]

Super, I'll look into it, thank you for your help and time.