Notes on Cambridge Maths

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Unbounded Diffusion Equation

We consider the diffusion equation

where and
We assume a recurrence of the form:

where

Fourier analysis of stability

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

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