Positivity-Preserving Numerical Methods for Belousov-Zhabotinsky Reaction

Yuro Adachi¹,   Novrianti¹, Okihiro Sawada²

¹Applied Physics Course, Faculty of Engineering, Gifu University, Gifu, Japan.
²Faculty of Engineering, Kitami Institute of Technology, Kitami, Japan.

DOI: 10.4236/am.2020.1110061                

Abstract

The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use a new successive approximation of solutions, ensuring its positivity. To obtain the positivity and invariant region for numerical solutions, the system is discretized as difference equations of explicit form, employing operator splitting methods with linear stability conditions. Algorithm to solve the alternate solution is given.

Keywords

Positive Solution, Difference Equation, Belousov-Zhabotinsky Reaction, Invariant Region, Maximum Principle

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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