Preservation of the invariants of Lotka-Volterra equations by iterated deferred correction methods

Murat Uzunca

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arXiv · 1901.03870

Preservation of the invariants of Lotka-Volterra equations by iterated deferred correction methods

Murat Uzunca

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Abstract

In this paper we apply Kahan's nonstandard discretization to three dimensional Lotka-Volterra equations in bi-Hamiltonian form. The periodicity of the solutions and all polynomial and non-polynomial invariants are well preserved in long-term integration. Applying classical deferred correction method, we show that the invariants are preserved with increasing accuracy as a results of more accurate numerical solutions. Substantial speedups over the Kahan's method are achieved at each run with deferred correction method.

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Murat Uzunca. 2019-01-12. Preservation of the invariants of Lotka-Volterra equations by iterated deferred correction methods. https://arxiv.org/abs/1901.03870

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