On error growth functions of Runge-Kutta methods

DOI10.1016/S0168-9274(96)00032-3zbMath0871.65071MaRDI QIDQ5961741

Ernst Hairer, Marino Zennaro

Publication date: 1 October 1997

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

asymptotic stabilityRunge-Kutta method\(B\)-stabilityerror growth functionstiff differential equationsuperexponential functions

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Multiple scale methods for ordinary differential equations (34E13)

Related Items (9)

Efficient Stability-Preserving Numerical Methods for Nonlinear Coercive Problems in Vector Space ⋮ Stability and Convergence of Stepsize-Dependent Linear Multistep Methods for Nonlinear Dissipative Evolution Equations in Banach Space ⋮ Backward Euler discretization of fully nonlinear parabolic problems ⋮ Stability of continuous Runge-Kutta-type methods for nonlinear neutral delay-differential equations ⋮ Operator splitting implicit integration factor methods for stiff reaction-diffusion-advection systems ⋮ Nonlinear stability of general linear methods for neutral delay differential equations ⋮ Numerical stability of nonlinear delay differential equations of neutral type ⋮ Long-term stability of variable stepsize approximations of semigroups ⋮ Runge-Kutta methods in elastoplasticity

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on B-stability of Runge-Kutta methods
• Solving Ordinary Differential Equations I
• Non-linear stability of a general class of differential equation methods
• Stability Criteria for Implicit Runge–Kutta Methods
• Model Problems in Numerical Stability Theory for Initial Value Problems

This page was built for publication: On error growth functions of Runge-Kutta methods