Symbolic implementation of the algorithm for calculating Adomian polynomials

In this paper, a symbolic implementation code is developed of a technique proposed by Wazwaz [Appl. Math. Comput. 111 (2000) 53] for calculating Adomian polynomials for nonlinear operators. The algorithm proposed by him [Appl. Math. Comput. 111 (2000) 53] offers a promising approach for calculating...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 146; no. 1; pp. 257 - 271
Main Authors: Choi, H.-W., Shin, J.-G.
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 30.12.2003
Elsevier
Subjects:
Adomian decomposition method
Adomian polynomials
Algorithmics. Computability. Computer arithmetics
Applied sciences
Artificial intelligence
Computer science; control theory; systems
Exact sciences and technology
Mathematica
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Nonlinear evolution equation
Nonlinear operators
Numerical analysis. Scientific computation
Pattern matching
Pattern recognition. Digital image processing. Computational geometry
Sciences and techniques of general use
Theoretical computing
Mathematica
Nonlinear evolution equation
Adomian polynomials
Adomian decomposition method
Pattern matching
Nonlinear operators
Non linear equation
Adomian polynomial
Applied mathematics
Decomposition method
Evolution equation
Computer algebra
Adomian method
Non linear operator
ISSN:0096-3003, 1873-5649
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Summary:In this paper, a symbolic implementation code is developed of a technique proposed by Wazwaz [Appl. Math. Comput. 111 (2000) 53] for calculating Adomian polynomials for nonlinear operators. The algorithm proposed by him [Appl. Math. Comput. 111 (2000) 53] 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. 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. The symbolic implementation code author developed (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.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(02)00541-6