Topological structure preserving numerical simulations of dynamical models

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Authors

Anguelov, Roumen
Popova, Evgenija D.

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Publisher

Elsevier

Abstract

This paper brings together two methods producing numerical solutions with a statement of their quality - the nonstandard finite difference method and the method of validated computing. It deals with the construction and the analysis of reliable numerical discretizations of dynamical systems by employing these two techniques. An epidemiological model is used as a model example for their combined application.

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Keywords

Nonstandard finite difference method, Validated computing, Dynamic consistency

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Citation

R. Anguelov, E.D. Popova, Topological structure preserving numerical simulations of dynamical models, Journal of Computational and Applied Mathematics (2010), doi:10.1016/j.cam.2010.05.038