Modified Adomian Method through Efficient Inverse Integral Operators to Solve Nonlinear Initial-Value Problems for Ordinary Differential Equations

The present manuscript examines different forms of Initial-Value Problems (IVPs) featuring various types Ordinary Differential Equations (ODEs) by proposing a proficient modification to the famous standard Adomian decomposition method (ADM). paper collected inverse integral operators and further successfully demonstrated their applicability on dissimilar nonlinear singular nonsingular ODEs. Furthermore, we surveyed most cases in this very new method, it was found have fast convergence rate and, other hand, high precision whenever exact analytical solutions are reachable.