TITLE:
Positivity-Preserving Numerical Methods for Belousov-Zhabotinsky Reaction
AUTHORS:
Yuro Adachi, Novrianti, Okihiro Sawada
KEYWORDS:
Positive Solution, Difference Equation, Belousov-Zhabotinsky Reaction, Invariant Region, Maximum Principle
JOURNAL NAME:
Applied Mathematics,
Vol.11 No.10,
October
9,
2020
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.