I have to prove that the two steps of a time split scheme have amplification factors that commute with each other, then the time split scheme is stable if each step is stable.
I have
u_t + Au +Bu=0 [u_t is the partial derivative of u with respect to t]
I need to show that if AB = BA where A and B are matrices then the time split scheme is stable. I understand the idea, but not how to set it up.
Thanks.