NAPA: Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions. he Adomian decomposition method is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems
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References in zbMATH (referenced in 4 articles )
Showing results 1 to 4 of 4.
- Yu, Jianping; Jing, Jian; Sun, Yongli; Wu, Suping: ((n + 1))-dimensional reduced differential transform method for solving partial differential equations (2016)
- Dalir, Nemat: Modified decomposition method with new inverse differential operators for solving singular nonlinear IVPs in first- and second-order PDEs arising in fluid mechanics (2014)
- Yun, Yin-Shan; Chaolu, Temuer; Duan, Jun-Sheng: A segmented and weighted Adomian decomposition algorithm for boundary value problem of nonlinear groundwater equation (2014)
- Lin, Yezhi; Liu, Yinping; Li, Zhibin: Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions (2012)