MODIFIED RUNGE-KUTTA ALGORITHM FOR OSCILLATORYCHEMICAL KINETICS

Abstract

Oscillatory dynamics frequently arise in the kinetics of chemical
reactions, posing significant challenges to traditional numerical methods in capturing the dynamics. In this study, we introduce a class of modified Runge Kutta methods specifically designed to solve such oscillatory chemical kinetics problems. Based on exponential fitting conditions for Runge-Kutta methods, we adapt several classical Runge-Kutta methods to better accommodate oscillatory behaviour. Three distinct classes of these modified methods based on some choosen parameters are proposed and presented. To evaluate their effectiveness, we conduct numerical experiments on two practical problems characterised by oscillatory chemical reactions. The results clearly demonstratethat the modified Runge-Kutta methods outperform their classical counterparts when applied to oscillatory systems.