A systematic review for modeling of physical problems for differential equations via Newton-Raphson based Laplace Adomian decomposition method

Abstract

The Newton-Raphson based Laplace-Adomian Decomposition Method  is an effective analytical technique used to solve nonlinear differential equations. It combines the power of the Laplace transform and the Adomian decomposition method coupled with Newton-Raphson method to provide an approximate solution in the form of a rapidly convergent series. The method begins by applying the Laplace transform to convert the original differential equation into an algebraic form, which is then solved using the modified Adomian decomposition. The solution is expressed as a series, and the terms are computed iteratively using Adomian polynomials. This paper reviews the principles, applications, advantages, and limitations of modified Laplace Adomian decomposition method, highlighting its potential as a powerful tool for solving complex differential equations in various fields.