Bibliographic Details
| Title: |
Backward Analysis Of Numerical Integrators And Symplectic Methods |
| Authors: |
Ernst Hairer |
| Contributors: |
The Pennsylvania State University CiteSeerX Archives |
| Superior Title: |
http://www.unige.ch/math/biblio/preprint/symplect.ps. |
| Publisher Information: |
Springer-Verlag |
| Publication Year: |
1994 |
| Collection: |
CiteSeerX |
| Subject Terms: |
Key words. Backward analysis, Hamiltonian systems, Runge-Kutta methods, symplectic methods, P-series |
| Description: |
A backward analysis of integration methods, whose numerical solution is a Pseries, is presented. Such methods include Runge-Kutta methods, partitioned Runge-Kutta methods and Nystrom 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). Key words. Backward analysis, Hamiltonian systems, Runge-Kutta methods, symplectic methods, P-series. 1. Introduction For the numerical solution of ordinary differential equations y 0 = f(y) (1:1) we consider one-step integrators such as Runge-Kutta methods or something similar. The . |
| Document Type: |
text |
| File Description: |
application/postscript |
| Language: |
English |
| Relation: |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.8870; http://www.unige.ch/math/biblio/preprint/symplect.ps |
| Availability: |
http://www.unige.ch/math/biblio/preprint/symplect.ps |
| Rights: |
Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
| Accession Number: |
edsbas.B2759A1E |
| Database: |
BASE |
