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Backward Error Analysis for Numerical Integrators (1996)
| Venue: | SIAM J. Numer. Anal |
| Citations: | 111 - 7 self |
BibTeX
@ARTICLE{Reich96backwarderror,
author = {Sebastian Reich},
title = {Backward Error Analysis for Numerical Integrators},
journal = {SIAM J. Numer. Anal},
year = {1996},
volume = {36},
pages = {1549--1570}
}
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Abstract
We consider backward error analysis of numerical approximations to ordinary differential equations, i.e., the numerical solution is formally interpreted as the exact solution of a modified differential equation. A simple recursive definition of the modified equation is stated. This recursion is used to give a new proof of the exponentially closeness of the numerical solutions and the solutions to an appropriate truncation of the modified equation. We also discuss qualitative properties of the modified equation and apply these results to the symplectic variable step-size integration of Hamiltonian systems, the conservation of adiabatic invariants, and numerical chaos associated to homoclinic orbits. 3 S. Reich, Backward error analysis 4
Keyphrases
backward error analysis modified equation numerical integrator numerical solution numerical chaos hamiltonian system appropriate truncation adiabatic invariant ordinary differential equation numerical approximation qualitative property new proof simple recursive definition symplectic variable step-size integration exact solution modified differential equation
