Derivation of the Classical Fourth Order Runge-Kutta Method

The classical fourth order Runge-Kutta method is among the most widely used numerical methods for obtaining the approximate solution of a first order initial-value problem, yet its derivation is often omitted from undergraduate texts on numerical methods because of the considerable algebra involved in arriving at the formulas. This article presents a detailed step-by-step derivation of the classical fourth order Runge-Kutta method.