A reliable modification of Adomian decomposition method. (English) Zbl 0928.65083

Wazwaz, Abdul-Majid

Appl. Math. Comput. 102, No. 1, 77-86 (1999).

The purpose of this paper is to show that, although the modified technique needs only a slight variation from the standard Adomian method, the results are improved and the convergence of the series solution is accelerated. Some illustrative examples are treated proving the performance of the modified algorithms.
This interesting paper has some relationships with results previously published by K. Abbaoui and Y. Cherruault [cf. Comput. Math. Appl. 28, No. 5, 103-109 (1995; Zbl 0809.65073)]. These works proved that when the Adomian method did not converge a change in the first term of the series solution could involve the convergence of the technique. Furthermore, it has also be proved that the convergence was accelerated by modifying the choice of the first term.
The author also asserts that his method minimizes the size of calculation needed. This is possible but not proved in this paper. May be that a good choice of the decomposition \(f= f_1+ f_2\) could minimize the calculations size. It would be an interesting following of the present paper.

Reviewer: Yves Cherruault (Paris)

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

Adomian decomposition method; accelerated convergence; noise terms; nonlinear differential and integral equations; numerical examples

Citations:

Zbl 0809.65073

References:

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