Stability limit of one-implicit-direction diffusion splitting
= Stability limit of one-implicit-direction diffusion splitting
On the $m$ by $m$ Dirichlet grid with $h=1/(m+1)$, the exact discrete stability condition for $m>1$ is
$$
0<\mu\leq\frac1{2\cos(\pi h)}.
$$
The mesh-independent sufficient condition is $0<\mu\leq1/2$, and the exact bound tends to $1/2$ as $h\to0$.