Backward analysis of numerical integrators and symplectic methods

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Reference

Backward analysis of numerical integrators and symplectic methods

HAIRER, Ernst

Abstract

A backward analysis of integration methods, whose numerical solution is a P-series, is presented. Such methods include Runge-Kutta methods, partitioned Runge-Kutta methods and Nystr"om methods. It is shown that the numerical solution can formally be interpreted as the exact solution of a perturbed differential system whose right-hand side is again a P-series.

The main result of this article is that for symplectic integrators applied to Hamiltonian systems the perturbed differential equation is a Hamiltonian system too. The proofs use the one-to-one correspondence between rooted trees and the expressions appearing in the Taylor expansions of the exact and numerical solutions (elementary differentials).

HAIRER, Ernst. Backward analysis of numerical integrators and symplectic methods. Annals of Numerical Mathematics , 1994, vol. 1, p. 107-132

Available at:

http://archive-ouverte.unige.ch/unige:12640

Disclaimer: layout of this document may differ from the published version.

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