Exactly Conservative Integrators

1995/07/31 by B. A. Shadwick, Shadwick, B. A., John C. Bowman +3
Earth and Planetary Sciences · Mathematics · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Biology Tumor Growth #Meteorological Phenomena and Simulations #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.chao-dyn/9507012

openalex publication_date 1995/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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