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

## TL;DR

This paper demonstrates that applying iterated deferred correction methods to Kahan's discretization of 3D Lotka-Volterra equations preserves invariants and periodicity more accurately, while significantly speeding up computations.

## Contribution

It introduces a novel combination of Kahan's discretization with deferred correction methods to enhance invariant preservation and computational efficiency in Lotka-Volterra systems.

## Key findings

- Invariants are preserved with increasing accuracy using deferred correction.
- The method achieves substantial speedups over Kahan's original method.
- Periodic solutions remain well-preserved over long-term integration.

## 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.