International Journal of Applied and Computational Mathematics | 2021
Modified Decomposition Method Based on Natural Transform for Solving Nonlinear Differential Equations Using Newton–Raphson Scheme
Abstract
In this article, we adopt the modified decomposition method (MDM) to find definite results of three different types of first order nonlinear ordinary differential equations that involves algebraic and transcendental functions and one second order ODE together with initial conditions. The MDM involves techniques of the natural transform method and also the algorithm of Adomian’s decomposition method in which Adomian’s polynomial is modified by involving Newton–Raphson scheme. We determine the series solutions by using MDM for each problem that converges to the exact solutions.