Exactly Conservative Integrators

Details Exactly Conservative Integrators Exactly Conservative Integrators

1995-08-03

arxiv.org/abs/chao-dyn/9507012v1

Nonlinear Sciences

Chaotic Dynamics

30 pages, postscript (1.3MB). Submitted to SIAM J. Sci. Comput.

Scientific paper

Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves these invariants. We illustrate the general method by applying it to the three-wave truncation of the Euler equations, the Lotka--Volterra predator--prey model, and the Kepler problem. This method is discussed in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.

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