We consider the diffusion equation
where
where
Fourier analysis of stability
Euler
has amplification factor:
this the method is stable iff
Reverse Euler
has amp:
thus is stable for all
Crank-Nicolson
has amp:
So stable for all
We consider the diffusion equation
where
where
has amplification factor:
this the method is stable iff
has amp:
thus is stable for all
has amp:
So stable for all