Topological structure preserving numerical simulations of dynamical models

Authors:
Roumen Anguelov;Evgenija D. Popova
Affiliations:
Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa;Institute of Mathematics and Informatics, Acad. G. Bonchev street, block 8, 1113 Sofia, Bulgaria
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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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.