Semi-Numerical Method for the Solution of System of Ordinary Differential Equation

Abstract

In this study, system of ordinary differential equation (ODE) with initial conditions have been solved using differential transform method (DTM). Maple 2023 was employed to obtain approximate solutions, highlighting DTM's efficiency in reducing computational efforts and saving time. Comparative analyses with Adomian decomposition method (ADM) and Runge-Kutta method (RK4) were conducted to evaluate DTM's accuracy. The results suggest that DTM's efficacy depends on equation characteristics and the number of terms used. A limited number of DTM terms are recommended for satisfactory approximations. DTM successfully solved one example, underscoring its simplicity and efficiency in handling differential problems with minimal computational workload.