Necessary conditions for the appearance of noise terms in decomposition solution series. (English) Zbl 0882.65132

Wazwaz, Abdul-Majid

Appl. Math. Comput. 81, No. 2-3, 265-274 (1997).

The author studies the problem of noise terms that appears in the series solution of the Adomian method. The main result is that the nonhomogeneity condition is not sufficient for obtaining noise terms. Another necessary condition is: the occurrence of the exact solution in the zeroth component.
From my point of view this result is included in a more general one. Indeed we have convergence results and we know that the choice of the first term of the series \((u_0)\) is fundamental for proving convergence. Convergence will derive from the choice of \(u_0\).

Reviewer: Y.Cherruault (Paris)

MSC:

65R20	Numerical methods for integral equations
45B05	Fredholm integral equations

Keywords:

decomposition solution series; convergence; noise terms; Adomian method

References:

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