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

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Murat Uzunca

Numerical Analysis · Submitted 12 Jan 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The periodicity of the solutions and all polynomial and non-polynomial invariants are well preserved in long-term integration.

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arXiv ID1901.03870 (version 2)
Pith IDTWG3HA3W, Pith's permanent record of this paper and its review
CitationMurat Uzunca. "Preservation of the invariants of Lotka-Volterra equations by iterated deferred correction methods." arXiv:1901.03870 (2019). https://pith.science/paper/TWG3HA3W
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arXiv listing abstract v2. Results and the main claim are underlined; .

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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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we apply Kahan's nonstandard discretization to three dimensional Lotka-Volterra equations in bi-Hamiltonian form. contribution 0.56 0.92 0.05 asserted 0.95
s1 The periodicity of the solutions and all polynomial and non-polynomial invariants are well preserved in long-term integration. result 1.00 0.79 0.59 asserted 1.00
s2 Applying classical deferred correction method, we show that the invariants are preserved with increasing accuracy as a results of more accurate numerical solutions. result 0.75 0.92 0.20 asserted 1.00
s3 Substantial speedups over the Kahan's method are achieved at each run with deferred correction method. result 1.00 0.91 0.17 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.55 · evidence from simulation or computation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original 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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