Article citationsMore>>

Furihata, D. and Matsuo, T. (2011) Discrete Variational Derivative Method. A Structure-Preserving Numerical Method for Partial Differential Equations. CRC Press, Boca Raton, FL.
https://doi.org/10.1201/b10387

has been cited by the following article:

• 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.