Long-term stability of variable stepsize approximations of semigroups

Nikolai Bakaev, Alexander Ostermann
2001 Mathematics of Computation  
This paper is concerned with the stability of rational one-step approximations of C 0 semigroups. Particular emphasis is laid on long-term stability bounds. The analysis is based on a general Banach space framework and allows variable stepsize sequences. Under reasonable assumptions on the stepsize sequence, asymptotic stability bounds for general C 0 semigroups are derived. The bounds are typical in the sense that they contain, in general, a factor that grows with the number of steps. Under
more » ... of steps. Under additional hypotheses on the approximation, more favorable stability bounds are obtained for the subclass of holomorphic semigroups.
doi:10.1090/s0025-5718-01-01389-8 fatcat:ke6wfwsztvaeresdvet6ggfpvm