Numerical flow-box theorems under structural assumptions

Barnabas M. Garay, L. P. Simon

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The numerical flow-box theorem says that locally, in the vicinity of nonequilibria, discretized solutions of an autonomous ordinary differential equation are exact solutions of a modified equation nearby: for stepsize h sufficiently small the original discretization operator is the time-h map of the solution operator of the modified equation. It is shown that the very same result holds true in the following categories of differential equations and discretizations: I/ preserving a finite number of first integrals; V/ preserving the volume form; S/ preserving the canonical symplectic form.

Original languageEnglish
Pages (from-to)733-749
Number of pages17
JournalIMA Journal of Numerical Analysis
Volume21
Issue number3
DOIs
Publication statusPublished - Jul 2001

Fingerprint

Modified Equations
Ordinary differential equations
Differential equations
Discretization
Symplectic Form
First Integral
Operator
Theorem
Non-equilibrium
Ordinary differential equation
Exact Solution
Differential equation
Form

Keywords

  • Flow-box
  • Perfectly modified equation
  • Symplectic discretization

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Numerical flow-box theorems under structural assumptions. / Garay, Barnabas M.; Simon, L. P.

In: IMA Journal of Numerical Analysis, Vol. 21, No. 3, 07.2001, p. 733-749.

Research output: Contribution to journalArticle

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