PRESERVATION OF THE INVARIANTS OF LOTKA-VOLTERRA EQUATIONS BY ITERATED DEFERRED CORRECTION METHODS

PRESERVATION OF THE INVARIANTS OF LOTKA-VOLTERRA EQUATIONS BY ITERATED DEFERRED CORRECTION METHODS

M. 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.

Keywords

Lotka-Volterra equations, conserved quantities, Kahan's method, iterated deferred correction.