Preservation of the invariants of Lotka-Volterra equations by iterated deferred correction methods
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866909652641382400 |
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| author | Uzunca, Murat |
| author_facet | Uzunca, Murat |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1901_03870 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Preservation of the invariants of Lotka-Volterra equations by iterated deferred correction methods Uzunca, Murat Numerical Analysis 65P10, 65L12 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. |
| title | Preservation of the invariants of Lotka-Volterra equations by iterated deferred correction methods |
| topic | Numerical Analysis 65P10, 65L12 |
| url | https://arxiv.org/abs/1901.03870 |