Convergence of linear multistep and one-leg methods for stiff nonlinear initial value problems

DOI10.1007/BF01952789zbMath0724.65071MaRDI QIDQ758135

B. I. Steininger, Willem H. Hundsdorfer

Publication date: 1991

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

linear multistep methodsorders of convergencevariable stepsizeone-leg methodsGlobal error boundsstiff nonlinear initial value problems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Multiple scale methods for ordinary differential equations (34E13)

Related Items (12)

Entropy dissipative one‐leg multistep time approximations of nonlinear diffusive equations ⋮ Two classes of implicit-explicit multistep methods for nonlinear stiff initial-value problems ⋮ The effect of the stopping of the Newton iteration in implicit linear multistep methods ⋮ One-leg variable-coefficient formulas for ordinary differential equations and local-global step size control ⋮ Fully-geometric mesh one-leg methods for the generalized pantograph equation: approximating Lyapunov functional and asymptotic contractivity ⋮ An efficient IMEX method for nonlinear functional differential equations with state-dependent delay ⋮ Stability and convergence analysis of implicit–explicit one-leg methods for stiff delay differential equations ⋮ Optimal convergence orders of fully geometric mesh one-leg methods for neutral differential equations with vanishing variable delay ⋮ One-leg methods for nonlinear stiff fractional differential equations with Caputo derivatives ⋮ Linear multistep methods as irreducible general linear methods ⋮ A Variable Stepsize, Variable Order Family of Low Complexity ⋮ Stability and error analysis of one-leg methods for nonlinear delay differential equations

Uses Software

• RODAS

Cites Work

• A study of B-convergence of Runge-Kutta methods
• Matrix valued versions of a result of von Neumann with an application to time discretization
• B-convergence of the implicit midpoint rule and the trapezoidal rule
• Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
• Choices in contractivity theory
• Contractivity in the numerical solution of initial value problems
• Stability of Two-Step Methods for Variable Integration Steps
• G-stability is equivalent toA-stability
• On One-Leg Multistep Methods
• Stability Properties of Implicit Runge–Kutta Methods
• Multiplier techniques for linear multistep methods
• Contractive methods for stiff differential equations part I
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