A new algorithm for solving differential equations

摘要

Different analytic methods have been proposed to solve differential equations, so far. In this paper, a novel analytic method that efficiently solves ODEs is presented. This method requires only the calculation of the first Adomian polynomial, namely A _0, and does not need to solve the functional equation in each iteration, as well as provides less computational work than other existing methods. Some important ordinary differential equations including the Lane-Emden equation of index m, the logistic nonlinear differential equation, and the Riccati equation are considered to illustrate the efficiency of the proposed algorithm.