Numerical Verification of the Order of Accuracy of a Runge-Kutta-Fehlberg Method in Solving an SEIR Model

Abstract

A Runge-Kutta-Fehlberg method (RKF45) is considered to solve an SEIR (Susceptible-Exposed-Infected-Recovered) mathematical model for infectious disease transmission. This numerical method is of the Runge-Kutta class, and has theoretical order of accuracy four and five depending on the involved formulations. We limit our problem to the RKF45 formula having theoretical order five. It is important to understand the behavior of RKF45 in solving an initial value problem, especially when implemented for real problems. In this paper, we take an SEIR mathematical model in our case, because this model is applicable in the prediction of infectious disease transmission in real life. Our research method is quantitative. We record the errors of numerical simulations. From the error values, we determine the numerical order of accuracy. Our research results show that RKF45 produces numerical order of accuracy five for the time step is sufficiently small. Therefore, the numerical order of accuracy matches with the theoretical one.