Stability of Rational Multistep Approximations of Holomorphic Semigroups
C. Palencia · Mathematics of Computation · 1995
In this paper we prove the stability of semidiscretizations in time of holomorphic semigroups in Banach spaces by means of ${\text {A}}(\alpha )$-stable rational multistep methods. No assumptions on the method other than ${\text {A}}(\alpha )$-stability are required. Our result is applicable in the maximum norm analysis of parabolic problems.