A note on multistep methods and attracting sets of dynamical systems

DOI10.1007/BF01405195zbMath0668.65059OpenAlexW1966132321MaRDI QIDQ1118363

Jens Lorenz, Peter E. Kloeden

Publication date: 1990

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

Full work available at URL: https://eudml.org/doc/133420

zbMATH Keywords

stabilityLyapunov functionmultistep methodsdiscrete time dynamical systemuniformly asymptotically stable attractor

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Dynamical systems and ergodic theory (37-XX)

Related Items (9)

General linear methods: Connection to one step methods and invariant curves ⋮ On the discretization of a partial differential equation in the neighborhood of a periodic orbit ⋮ On the stability of numerical methods of Hopf points using backward error analysis ⋮ Global dynamics of a discontinuous Galerkin approximation to a class of reaction-diffusion equation ⋮ Global dynamical properties of Euler and backward Euler ⋮ Matrix differential equations: a continuous realization process for linear algebra problems ⋮ Conserving first integrals under discretization with variable step size integration procedures ⋮ Feedback integrators ⋮ Upper Semicontinuity of Attractors for Linear Multistep Methods Approximating Sectorial Evolution Equations

Cites Work

• What do multistep methods approximate?
• Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations
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