A MAPLE package of new ADM-Padé approximate solution for nonlinear problems. Based on the new definition of four classes of Adomian polynomials proposed by Rach in 2008, a MAPLE package of new Adomian-Padé approximate solution for solving nonlinear problems is presented. This package combines the merits of the Adomian decomposition method and the diagonal Padé technique, and may give more accurate solutions of nonlinear problems with strong nonlinearity. Besides, the package is user-friendly and efficient, one only needs to input the initial conditions, governing equation and four optional parameters, then our package will output the analytic approximate solution within a few seconds, where the equation is decomposed into three parts, they are the linear term R, nonlinear term NN and source function g, which are all in functional form. Meanwhile, several graphs generated from the above solutions are displayed and demonstrate a favorable comparison. In this paper, several different types of examples are given to illustrate the validity and promising flexibility of the package. This package provides us with a convenient and useful tool for dealing with nonlinear problems, as well as its electronic version is free to download via the journal website.
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References in zbMATH (referenced in 8 articles , 1 standard article )
Showing results 1 to 8 of 8.
- Lin, Yezhi; Liu, Yinping; Li, Zhibin: Symbolic computation of analytic approximate solutions for nonlinear differential equations with boundary conditions (2013)
- Zeng, Yi: The Laplace-Adomian-Padé technique for the ENSO model (2013)
- Blanco-Cocom, Luis; Estrella, Angel G.; Avila-Vales, Eric: Solving delay differential systems with history functions by the Adomian decomposition method (2012)
- Noghrehabadi, Aminreza; Ghalambaz, Mohammad; Ghanbarzadeh, Afshin: A new approach to the electrostatic pull-in instability of nanocantilever actuators using the ADM-Padé technique (2012)
- Chu, Hongmei; Zhao, Yinlong; Liu, Yinping: A Maple package of new ADM-Padé approximate solution for nonlinear problems (2011)
- Duan, Jun-Sheng: New recurrence algorithms for the nonclassic Adomian polynomials (2011)
- Duan, Jun-Sheng: New ideas for decomposing nonlinearities in differential equations (2011)
- Duan, Jun-Sheng; Rach, Randolph: A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations (2011)