Long-term stability of variable stepsize approximations of semigroups

DOI10.1090/S0025-5718-01-01389-8zbMath1005.65076OpenAlexW1966104123MaRDI QIDQ3147175

Alexander Ostermann, Nikolai Yu. Bakaev

Publication date: 18 September 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-01-01389-8

zbMATH Keywords

asymptotic stabilityvariable stepsizelong-term stabilityapproximation of semigroups

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (6)

Decay rate of \(\exp (A^{-1}t)A^{-1}\) on a Hilbert space and the Crank-Nicolson scheme with smooth initial data ⋮ Stability of linear multistep methods and applications to nonlinear parabolic problems. ⋮ On the Crank-Nicolson scheme once again ⋮ On positivity, shape, and norm-bound preservation of time-stepping methods for semigroups ⋮ \(A\)-stable Runge-Kutta methods for semilinear evolution equations ⋮ On the convergence of rational approximations of semigroups on intermediate spaces

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• Semidiscretization in Time for Parabolic Problems
• On Rational Approximations of Semigroups
• On the Stability of Variable Stepsize Rational Approximations of Holomorphic Semigroups
• Analytic semigroups and optimal regularity in parabolic problems
• On error growth functions of Runge-Kutta methods

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