General linear methods: Connection to one step methods and invariant curves

DOI10.1007/BF01388696zbMath0810.65076OpenAlexW2006494867MaRDI QIDQ1326413

Daniel Stoffer

Publication date: 18 May 1994

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133712

zbMATH Keywords

attractorsinvariant curveslinear methodsmultivalue methodsone step methodshyperbolic periodic solutions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) 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)

Related Items (10)

On the stability of numerical methods of Hopf points using backward error analysis ⋮ Variable steps for reversible integration methods ⋮ Underlying one-step methods and nonautonomous stability of general linear methods ⋮ The cohesiveness of G-symplectic methods ⋮ Two-Derivative Error Inhibiting Schemes and Enhanced Error Inhibiting Schemes ⋮ On C^j-closeness between the solution flow and its numerical approximation ⋮ Error propagation of general linear methods for ordinary differential equations ⋮ Upper Semicontinuity of Attractors for Linear Multistep Methods Approximating Sectorial Evolution Equations ⋮ Symmetric general linear methods ⋮ General linear methods for ordinary differential equations

Cites Work

• Split linear multistep methods for the numerical integration of stiff differential systems
• Multi-step methods are essentially one-step methods
• Invariant curves of one-step methods
• What do multistep methods approximate?
• A note on multistep methods and attracting sets of dynamical systems
• On invariant closed curves for one-step methods
• Efficient Split Linear Multistep Methods for Stiff Ordinary Differential Equations
• Periodic solutions of finite difference equations
• Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations
• Invariant manifolds
• Unnamed Item

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