New method for calculating Adomian polynomials. (English) Zbl 1055.65068

Babolian, E.; Javadi, Sh.

Appl. Math. Comput. 153, No. 1, 253-259 (2004).

The Adomian method is used for solving nonlinear functional equations without discretization or linearization. This technique allows to obtain analytical solutions explicitly depending on time and state variables. The method is based on the calculus of special polynomials (called Adomian polynomials) and the authors give an original technique for obtaining these polynomials in a recurrent and simple way. This involves a routine derivation very similar to those for ordinary functions.

Reviewer: Yves Cherruault (Paris)

MSC:

65J15	Numerical solutions to equations with nonlinear operators
47J05	Equations involving nonlinear operators (general)
65Q05	Numerical methods for functional equations (MSC2000)

Keywords:

Adomian decomposition method; Adomian polynomials; nonlinear functional equations; analytical resolution; recurrent method; Nonlinear operators

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