COMPARATIVE ANALYSIS OF NUMERICAL SOLUTIONS OF EULER, RK-4, ABM-4 AND RKCoM4 METHODS OF INITIAL VALUE PROBLEMS IN NONHOMOGENEOUS SECOND ORDER DIFFERENTIAL EQUATIONS

Abstract

Non-homogeneous second-order differential equations are often used in various mathematical models in physics, engineering, and system dynamics. Numerical solutions are the main alternative when analytical solutions are difficult to obtain. This study compares the performance of the Euler, Runge-Kutta 4th order (RK-4), Adams-Bashforth-Moulton 4th order (ABM-4), and Runge-Kutta Contra Harmonic Mean 4 (RKCoM4) numerical methods in solving initial value problems (MNAs) in non-homogeneous second-order differential equations. The analysis was carried out by comparing the numerical calculation results of each method using the Mean Absolute Error (MAE) method. The results of numerical calculations and simulations show that the RK-4 and ABM4 methods provide higher accuracy than the Euler and RKCoM4 methods for 2 cases of non-homogeneous second-order differential equations.