Discrete gradient methods for solving ODEs numerically while preserving a first integral
- 7 July 1996
- journal article
- letter
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 29 (13) , L341-L349
- https://doi.org/10.1088/0305-4470/29/13/006
Abstract
We show that all direct methods for preserving a first integral during the numerical integration of an ordinary differential equation fit into the unified framework of discrete gradient methods. Using this framework we construct several new integral-preserving schemes.Keywords
This publication has 8 references indexed in Scilit:
- Construction of higher order symplectic integratorsPublished by Elsevier ,2002
- Variable steps for reversible integration methodsComputing, 1995
- Completely conservative, covariant numerical methodologyComputers & Mathematics with Applications, 1995
- Invariants and numerical methods for ODEsPhysica D: Nonlinear Phenomena, 1992
- Chaotic Evolution of the Solar SystemScience, 1992
- Hamiltonian-conserving discrete canonical equations based on variational difference quotientsJournal of Computational Physics, 1988
- Stability of Runge-Kutta Methods for Trajectory ProblemsIMA Journal of Numerical Analysis, 1987
- Product formulas and numerical algorithmsCommunications on Pure and Applied Mathematics, 1978