A COMPARATIVE STUDY ON NUMERICAL SOLUTIONS OF INITIAL VALUE PROBLEMS OF DIFFERENTIAL EQUATIONS USING THE THREE NUMERICAL METHODS

Abstract

Numerical methods are crucial for solving ordinary differential equations (ODEs) that frequently arise in various fields of science and engineering. This study compares three numerical methods: the fourth-order Runge-Kutta method (RK4), the fourth-order Runge-Kutta Contra-harmonic Mean method (CoM4), and the fourth-order Adam-Bashforth-Moulton method (ABM4) in solving initial value problems of ODEs. Three IVPs of ODEs have been solved with varying step sizes using the three methods that have been proposed, and the solutions for each step size are examined. Numerical comparisons between RK4, CoM4, and ABM4 methods have been presented to solve three initial problems of ODE. Simulation results show that each method has advantages and limitations depending on the type of ODE being solved. We find that for very small step sizes, the numerical solutions agree the best with the exact solution. As such, all three proposed approaches are sufficient to solve the IVP ODE accurately and efficiently. Among the three proposed methods, we observe that the mean absolute error for the RK4 method is the smallest, followed by the ABM4 method.