A nonstandard finite difference method for n-dimensional productive-destructive systems

Based on previous research by Dimitrov and Kojouharov, a class of dynamically consistent numerical methods are analysed for general -dimensional productive-destructive systems (PDS). Using this analysis, a methodology for constructing positive and elementary stable non-standard numerical methods is...

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Bibliographic Details
Published in:Journal of difference equations and applications 2015-03, Vol.21 (3), p.240-254
Main Authors: Wood, Daniel T., Dimitrov, Dobromir T., Kojouharov, Hristo V.
Format: Article
Language:English
Subjects:
92-08
Biological
Biology
Difference equations
Dynamical systems
Dynamics
elementary stable
finite difference
Finite difference method
Mathematical analysis
Mathematical models
non-standard
Numerical analysis
positivity
productive-destructive
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Summary:Based on previous research by Dimitrov and Kojouharov, a class of dynamically consistent numerical methods are analysed for general -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.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2014.997228