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Scientific article
English

The life-span of backward error analysis for numerical integrators

Contributors

Hairer, Ernst; Lubich, Christian

Published in

Numerische Mathematik, vol. 76, no. 4, p. 441-462

Publication date

1997

Abstract

Backward error analysis is a useful tool for the study of numerical approximations to ordinary differential equations. The numerical solution is formally interpreted as the exact solution of a perturbed differential equation, given as a formal and usually divergent series in powers of the step size. For a rigorous analysis, this series has to be truncated. In this article we study the influence of this truncation to the difference between the numerical solution and the exact solution of the perturbed differential equation. Results on the long-time behaviour of numerical solutions are obtained in this way. We present applications to the numerical phase portrait near hyperbolic equilibrium points, to asymptotically stable periodic orbits and Hopf bifurcation, and to energy conservation and approximation of invariant tori in Hamiltonian systems.

Keywords

  • Backward error analysis
  • Long-term integration
  • Hamiltonian systems
  • Hopf bifurcation

UNIGE affiliation entities

Citation (ISO format)

HAIRER, Ernst, LUBICH, Christian. The life-span of backward error analysis for numerical integrators. In: Numerische Mathematik, 1997, vol. 76, n° 4, p. 441–462. doi: 10.1007/s002110050271

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Article (Published version)

Identifiers

Additional URL for this publication

http://www.springerlink.com/content/l687gym3wxgx5f07/

Journal ISSN

0029-599X
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Technical informations

Creation

12/11/2010 14:44:00

First validation

12/11/2010 14:44:00

Update

14/03/2023 16:08:45

Status update

14/03/2023 16:08:45

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