Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-25T22:38:27.872Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximately preserving symmetries in the numerical integration of ordinary differential equations

Published online by Cambridge University Press:  01 October 1999

ARIEH ISERLES ,
ROBERT McLACHLAN  and
ANTONELLA ZANNA
ARIEH ISERLES
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, UK
ROBERT McLACHLAN
Affiliation:
Mathematics, Massey University, Private Bag 11-222, Palmerston North, New Zealand
ANTONELLA ZANNA
Affiliation:
Newnham College, University of Cambridge, Cambridge CB3 9DF, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a general procedure for recursively improving the invariance of a numerical integrator under a symmetry group. If h is a symmetry, we construct the adjoint method h−1h. In each time step we apply either the original method or the adjoint method, according to a prescription based on the Thue–Morse sequence. The outcome is a solution sequence which displays progressively smaller symmetry errors, to any desired order in the time-step. The method can also be used to force the solution to stay close to a desired submanifold of phase space, while retaining structural properties of the original method.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 10 , Issue 5 , October 1999 , pp. 419 - 445
Copyright
1999 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)