The general solution for singular equations of (n+1) order using Adomian decomposition method

Abstract

This article proposes a general and efficient modification of Adomain decomposition method (ADM) to obtain the general solutions for (n+1)- order nonlinear singular differential equations with different boundary conditions. This technique is proposed to overcome the singular behaviour of this type of problems. We study several nonlinear problems which will illustrate the efficiency of using that developed technique of the given method to clearly confirm the effectiveness and accuracy of ADM. In addition, we compare the numerical results with the exact solution to explain the rapid convergence of the approximation series as the solution.