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Positivity-Preserving Numerical Methods for Belousov-Zhabotinsky Reaction
Applied Physics Course, Faculty of Engineering, Gifu University, Gifu, Japan
Applied Physics Course, Faculty of Engineering, Gifu University, Gifu, Japan
Faculty of Engineering, Kitami Institute of Technology, Kitami, Japan
- 1 Applied Physics Course, Faculty of Engineering, Gifu University, Gifu, Japan
- 2 Applied Physics Course, Faculty of Engineering, Gifu University, Gifu, Japan
- 3 Faculty of Engineering, Kitami Institute of Technology, Kitami, Japan
Applied Mathematics·Volume 11 (2020)·Pages 943–950·Published 30 September 2020·DOI10.4236/am.2020.1110061
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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.
KeywordsPositive SolutionDifference EquationBelousov-Zhabotinsky ReactionInvariant RegionMaximum Principle
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