## Solving PDEs with FFT

Using the finite discrete Forier transform we can solve some problems for some partial differential equations.
• The heat equation $$u_t-u_{xx}=0$$ (heat.m).
• The Schrödinger evolution equation $$u_t-\sqrt{-1}u_{xx}=0$$ (schroedinger.m).
• The linear part of the Korteweg de Vries equation $$u_t+u_{xxx}=0$$ (lkdv.m).
• The Korteweg de Vries equation $$u_t+u_{xxx}+3(u^2)_x=0$$ (kdv.m).
• Burgers' equation $$u_t-u_{xx}+uu_x=0$$ (burgers.m).
• Inviscid Burgers' equation $$u_t+(u^2)_x/2=0$$ (iburgers.m).