COMPARISON OF NUMERICAL METHODS FOR SOLVING INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

Abstract

This research focuses on comparing several numerical methods for solving initial value problems for ordinary differential equations.We start by reviewing some of the fundamental concepts of differential equations and their solvability. Moreover, we address the numerical methods used to solve initial value problems, namely, the one-step and multistep methods. These include the Euler method, higher-order Taylor methods, Runge-Kutta methods, Runge-Kutta-Fehlberg method, and the Adams-Bashforth and Adams-Moulton methods. Their accuracy, stability and convergence are also investigated. These numerical methods are illustrated through some numerical examples. Numerical results show clearly that the Runge-Kutta methods, particularly RK4, RKF45, generally provide high accuracy, while multistep methods show good performance when used in a predictor-corrector approach. The measured orders of convergence are also in good agreement with the theoretical orders. Overall, the results demonstrate that the choice of a suitable numerical method depends on the characteristics of the problem and the required levels of accuracy and stability