Forward Euler diffusion scheme
= Forward Euler diffusion scheme
{c}
For the centered spatial second difference, forward Euler has the update
$$
u_m^{n+1}=\mu u_{m-1}^n+(1-2\mu)u_m^n+\mu u_{m+1}^n.
$$
It is stable for $0\leq\mu\leq1/2$. In this range the update is a convex combination, which gives a direct maximum-norm proof as well as the Fourier proof.