Nonstandard Finite-Difference Methods for Dynamical Systems in Biology

Authors

  • Hristo V Kojouharov The University of Texas at Arlington

DOI:

https://doi.org/10.11145/537

Abstract

A brief overview of the nonstandard finite-difference methods is presented. Next, using the nonstandard discretization approach, a positive and elementary stable numerical method is developed for productive-destructive systems. Finally, a nonstandard finite-difference method for general autonomous dynamical systems is constructed. The proposed numerical methods preserve the positivity of solutions and the local behavior of the corresponding dynamical systems near equilibria; and are also computationally efficient and easy to implement. Applications to select problems in biology are given to demonstrate the performance of the new methods.

Author Biography

Hristo V Kojouharov, The University of Texas at Arlington

Professor of Mathematics

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Published

2015-05-29

Issue

Vol. 2 No. 1 (2015)

Section

Conference Keynote Presentations

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