A Review of Analytical Algorithms for Approximate Solutions of Ordinary Differential Equation

This review article aims to provide an in-depth analysis of a wide range of analytical methods used for solving ordinary differential equations (ODEs). ODEs are fundamental in numerous scientific and engineering disciplines, making the development, and understanding of effective solution techniques crucial. We explore various approaches, including the Adomian decomposition method, homotopy perturbation method, homotopy analysis method, variational iteration method, Daftardar-Jafari method, successive approximation method, power series method, and modified Adomian decomposition method. Each method is discussed in terms of its principles, applications, advantages, limitations, and computational considerations. This comprehensive overview will serve as a valuable resource for researchers, practitioners, and students interested in solving ODEs.