zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Convergence of Adomian’s method. (English) Zbl 0697.65051
G. Adomian and his collaborators have developed in some papers a new method for solving nonlinear functional equations. The solution of this method is given by a series in which each term is a polynomial adapted to the nonlinearity and determined in a recurrent manner. In this paper the author proposes a new definition of the technique, in order to use results, as fixed point theorems, for proving convergence of the series and the fact that the sum of the series is the solution of the given equations. It is easy to see that the technique proposed is powerful and the use of this one is not difficult. The series solution converges with remarkable rapidity under some reasonable assumptions. When these assumptions cannot be true then a modified technique is proposed and so these approaches are better than most of the numerical methods, suggested in the literature, for solving nonlinear problems.
Reviewer: A.Donescu

65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
Full Text: DOI