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Zbl 1033.65036
Choi, H.-W.; Shin, J.-G.
Symbolic implementation of the algorithm for calculating Adomian polynomials. (English)
[J] Appl. Math. Comput. 146, No. 1, 257-271 (2003). ISSN 0096-3003

Summary: A symbolic implementation code is developed of a technique proposed by {\it A.-M. Wazwaz} [Appl. Math. Comput. 111, 53--69 (2000; Zbl 1023.65108)] for calculating Adomian polynomials for nonlinear operators. The algorithm proposed by him offers a promising approach for calculating Adomian polynomials for all forms of nonlinearity, but it is not easy to implement due to its huge size of algebraic calculations, complicated trigonometric terms, and unique summation rules. \par It is well known that the algebraic manipulation language such as Mathematica is useful to facilitate such a hard computational work. Pattern-matching capabilities peculiar feature of Mathematica are used in index regrouping which is a key role in constructing Adomian polynomials. The computer algebra software Mathematica is used to collect terms to their order and to simplify the terms. \par The symbolic implementation code developed by the author (appearing at appendix) has the flexibility that may easily cover any length of Adomian polynomial for many forms of nonlinear cases. A nonlinear evolution equation is investigated in order to justify the availability of symbolic implementation code.

MSC 2000:: *65J15 Equations with nonlinear operators (numerical methods)
68W30 Symbolic computation and algebraic computation
76N15 Gas dynamics, general
47J25 Methods for solving nonlinear operator equations (general)
35L60 First-order nonlinear hyperbolic equations
65M55 Multigrid methods; domain decomposition (IVP of PDE)
65M70 Spectral, collocation and related methods (IVP of PDE)

Keywords: Adomian decomposition method; Adomian polynomials; Nonlinear operators; Nonlinear evolution equation; Mathematica; Pattern matching; gas dynamics

Citations: Zbl 1023.65108

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