I am numarically solving a PDE using a Fourier Spectral method.
Basically it works in 1D:
u(t+dt) = iF(-iz^2dtF(u(t))
where F is my Fourier transform and iF is my inverse fourier transform. z is the wave number and dt the tie step.
so the second derivative coresponds to -iz^2dt (d^2u/dx^2)
How ill this look like in 2D? when I have:
d^2u/dx^2 + d^2u/dy^2
in my PDE?
Basically it works in 1D:
u(t+dt) = iF(-iz^2dtF(u(t))
where F is my Fourier transform and iF is my inverse fourier transform. z is the wave number and dt the tie step.
so the second derivative coresponds to -iz^2dt (d^2u/dx^2)
How ill this look like in 2D? when I have:
d^2u/dx^2 + d^2u/dy^2
in my PDE?