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English

Asymptotic expansions and backward analysis for numerical integrators

Contributors

Hairer, Ernst; Lubich, Christian

Published in

Rafael de la Llave; Linda R. Petzold & Jens Lorenz (Ed.), Dynamics of algorithms, p. 91-106

Publisher

New York : Springer

Collection

  • The IMA volumes in mathematics and its applications; 118

Publication date

2000

Abstract

For numerical integrators of ordinary differential equations we compare the theory of asymptotic expansions of the global error with backward error analysis. On a formal level both approaches are equivalent. If, however, the arising divergent series are truncated, important features such as the semigroup property, structure perservation and exponentially small estimates over long times are valid only for the backward error analysis. We consider one-step methods as well as multistep methods, and we illustrate the theoretical results on several examples. In particular, we study the preservation of weakly stable limit cycles by symmetric methods.

Keywords

  • Asymptotic expansions
  • Backward error analysis
  • One-step methods
  • Multistep methods
  • Long-time behavior

UNIGE affiliation entities

Citation (ISO format)

HAIRER, Ernst, LUBICH, Christian. Asymptotic expansions and backward analysis for numerical integrators. In: Dynamics of algorithms. Rafael de la Llave; Linda R. Petzold & Jens Lorenz (Ed.). New York : Springer, 2000. p. 91–106. (The IMA volumes in mathematics and its applications)

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Book chapter

Identifiers

  • PID : unige:12439
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Technical informations

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10/11/2010 13:59:00

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10/11/2010 13:59:00

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