The Derivation of Various Arbitrary Parameters in the Formulation of Classical Fourth-Order Runge-Kutta Method

Abstract

Many practical problems in engineering and science are formulated by Ordinary Differential Equations (ODE) that require their own numerical solution. Numerous methods, e.g., the Euler method, the modified Euler method, Heun’s method, the Adam-Bashforth method and so on, exist in the context of numerical analysis. Amongst them, the classical RungeKutta method (RK4) of the fourth order is mostly used. In this paper, we derive the value of different parameters in the formulation of the fourth order Runge-Kutta method explicitly. The determination techniques are shown stepwise in a straight-forward way. Basically, this paper provides a survey of previous work on deriving the fourth-order Runge-Kutta formula. The major goal of this paper is to provide more details on how to formulate the RK4 method explicitly in order to encourage further research into this method.