A modified numerical iterative algorithm of Adomian analytic solution for nonlinear differential equations

In this paper, a modified numerical iterative algorithm using Adomian Decomposition Method (ADM) for nonlinear differential equations is presented. Standard ADM could derive series solution with finite terms. The limited truncation order affects the convergence of the solution. The presented algorithm organises the solution in a matrix based on Differential Transformation (DT) theory and uses the coefficient matrix in each discrete interval iteratively to obtain numerical solution quickly. On this basis, maximum step-size criterion is proposed to make the numerical solution satisfy the recursion percent error. Comparisons with the exact solution or MATLAB@ ODE45 solution of two nonlinear examples have proved the validity of the proposed method for nonlinear differential equations. ©, 2015, Binary Information Press. All right reserved.