A COMPARATIVE ANALYSIS OF TWO SEMI ANALYTIC APPROACHES IN SOLVING SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS

Abstract

The resolution of systems of first-order ordinary differential equations (ODEs) is a critical endeavor with extensive applications in various scientific and engineering fields. This study presents a rigorous comparative assessment of two semi-analytic methodologies: the Variational Iterative Method (VIM) and the New Iterative Method (NIM). Addressing a significant research gap, our investigation explores the relative merits and demerits of these approaches. We provide a comprehensive examination of VIM, a well-established method, alongside NIM, a relatively less explored approach, to identify their comparative strengths and limitations. Furthermore, the study enriches existing knowledge in numerical methods for ODEs by highlighting essential performance characteristics such as convergence properties, computational efficiency, and accuracy across a diverse array of ODE systems. Through meticulous numerical experimentation, we uncover practical insights into the efficacy of VIM and NIM, bridging a critical knowledge gap in the field of numerical ODE solvers. Our findings demonstrate VIM as the more effective method, thereby enhancing the understanding of semi-analytic approaches for solving ODE systems and providing valuable guidance for practitioners and researchers in selecting the most appropriate method for their specific applications