Thirty years of G-stability

DOI10.1007/s10543-006-0078-8zbMath1105.65085OpenAlexW1970776832MaRDI QIDQ2433883

John C. Butcher

Publication date: 31 October 2006

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-006-0078-8

zbMATH Keywords

A-stabilityinitial value problemsnonlinear stabilityRunge-Kutta methodsstiff differential equationsgeneral linear methodsB-stability

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (8)

Construction of algebraically stable dimsims ⋮ Long-time behavior of numerical solutions to nonlinear fractional ODEs ⋮ Dahlquist's classical papers on stability theory ⋮ Search for highly stable two-step Runge-Kutta methods ⋮ Order conditions for general linear methods ⋮ Nordsieck methods with computationally verified algebraic stability ⋮ Exponential mean-square stability properties of stochastic linear multistep methods ⋮ Variable order and stepsize in general linear methods

Cites Work

• Linear and non-linear stability for general linear methods
• The equivalence of algebraic stability and AN-stability
• Runge-Kutta schemes for Hamiltonian systems
• Canonical Runge-Kutta methods
• Sur la B-stabilité des méthodes de Runge-Kutta
• Linear multistep methods as irreducible general linear methods
• Stability of Two-Step Methods for Variable Integration Steps
• G-stability is equivalent toA-stability
• Convergence and stability in the numerical integration of ordinary differential equations
• Non-linear stability of a general class of differential equation methods
• The Concept of B-Convergence
• Multiplier techniques for linear multistep methods
• A stability property of implicit Runge-Kutta methods
• Stability Criteria for Implicit Runge–Kutta Methods
• On the Convergence of Numerical Solutions to Ordinary Differential Equations
• A special stability problem for linear multistep methods
• Integration of Stiff Equations
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