# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
A reliable modification of Adomian decomposition method. (English) Zbl 0928.65083

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.

##### MSC:
 65L05 Initial value problems for ODE (numerical methods) 34A34 Nonlinear ODE and systems, general