Symbolic computation of analytic approximate solutions for nonlinear differential equations with boundary conditions

摘要

The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions. In this paper, based on the new definitions of the Adomian polynomials, and the double decomposition method, a new algorithm is proposed to construct analytic approximations for nonlinear differential equations with (coupled) boundary conditions. Furthermore, a MAPLE software package is developed to implement our new algorithm, which is user-friendly and efficient. One only needs to input the system, boundary conditions and several necessary parameters, then our package will deliver the analytic approximate solution within a few seconds. Several different types of nonlinear examples are given to illustrate the scope and demonstrate the validity of our software package, especially for nonlinear multi-order and multi-point boundary value problems. Our package provides a helpful and easy-to-use tool in science and engineering to deal with the most frequently encountered boundary value problems. This MAPLE package is free to download on the website: http://www.cs.ecnu.edu.cn/∼lizb/index.htm.