Numerical Solution Analysis Using The Runge-Kutta-Fehlberg Method on A Model of The Spread of Smoking Behavior

Abstract

We consider a mathematical model of the spread of smoking behavior in the population. The model is solved using the Runge-Kutta-Fehlberg numerical method. As smoking is not healthy in general, we are interested in the case of smoker-free in the long term of time. The equilibrium of the smoker-free is recalled and used to match the numerical simulation for large time values. In addition, our contribution in this paper is to verify that the Runge-Kutta-Fehlberg numerical method is fifth order in convergence. Using error tabulation, we show that the numerical method is indeed of the fifth order.