On the Stability of Variable Stepsize Rational Approximations of Holomorphic Semigroups
- 1 January 1994
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 62 (205) , 93-103
- https://doi.org/10.2307/2153397
Abstract
We consider variable stepsize time approximations of holomorphic semigroups on general Banach spaces. For strongly ${\text {A}}(\theta )$-acceptable rational functions a general stability theorem is proved, which does not impose any constraint on the ratios between stepsizes.Keywords
This publication has 15 references indexed in Scilit:
- A Stability Result for Sectorial Operators in Banach BpacesSIAM Journal on Numerical Analysis, 1993
- The stability of rational approximations of analytic semigroupsBIT Numerical Mathematics, 1993
- On resolvent conditions and stability estimatesBIT Numerical Mathematics, 1991
- Finite-Element Methods for a Strongly Damped Wave EquationIMA Journal of Numerical Analysis, 1991
- Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations.Mathematics of Computation, 1986
- An extension of the Lax-Richtmyer theoryNumerische Mathematik, 1984
- On Rational Approximations of SemigroupsSIAM Journal on Numerical Analysis, 1979
- High-Accuracy Stable Difference Schemes for Well-Posed Initial-Value ProblemsSIAM Journal on Numerical Analysis, 1979
- Besov Spaces and Applications to Difference Methods for Initial Value ProblemsMathematics of Computation, 1976
- Spectral measures, generalized resolvents, and functions of positive typeJournal of Mathematical Analysis and Applications, 1965