A nonstandard finite difference method forn-dimensional productive–destructive systems

2015/01/03 by Daniel T. Wood, Daniel Wood, Dobromir Dimitrov +2 · 1 citation
Mathematics · Medicine · #Fractional Differential Equations Solutions #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models

paper · doi:10.1080/10236198.2014.997228

openalex publication_date 2015/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Based on previous research by Dimitrov and Kojouharov, a class of dynamically consistent numerical methods are analysed for general n-dimensional productive–destructive systems (PDS). Using this analysis, a methodology for constructing positive and elementary stable non-standard numerical methods is established. The non-standard approach, pioneered by Mickens, results in qualitatively superior numerical methods when compared to the standard approach. PDS model a wide range of dynamical systems, including systems with biological, chemical and physical interactions. An application to a four-dimensional biological system is presented.

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