A Shadowing Lemma Approach to Global Error Analysis for Initial Value ODEs

DOI10.1137/0915058zbMath0818.65068OpenAlexW2075364537WikidataQ124810403 ScholiaQ124810403MaRDI QIDQ4305421

Erik S. Van Vleck, Shui-Nee Chow

Publication date: 13 October 1994

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1808/17289

zbMATH Keywords

dynamical systemsnumerical exampleserror boundsRunge-Kutta methodshadowing lemma

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) Error bounds for numerical methods for ordinary differential equations (65L70) Dynamical systems and ergodic theory (37-XX)

Related Items

SHADOWING PROPERTIES OF RANDOM HYPERBOLIC SETS ⋮ What good are numerical simulations of chaotic dynamical systems? ⋮ Shadowing orbits of ordinary differential equations on invariant submanifolds ⋮ A survey of shadowing methods for numerical solutions of ordinary differential equations ⋮ A numerical \(C^{1}\)-shadowing result for retarded functional differential equations

Uses Software

• svdpack