One-implicit-direction diffusion splitting
= One-implicit-direction diffusion splitting
The split step
$$
(I-\mu A_y)u^{n+1/2}=u^n,
\qquad
u^{n+1}=(I+\mu A_x)u^{n+1/2}
$$
has amplification matrix
$$
C=(I+\mu A_x)(I-\mu A_y)^{-1}.
$$
On a common directional eigenvector its eigenvalue is $(1+\mu\lambda_p)/(1-\mu\lambda_q)$.