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)
A new algorithm for calculating Adomian polynomials. (English) Zbl 1087.65528
Summary: A new algorithm for calculating Adomian polynomials for nonlinear operators will be established by parametrization. The algorithm requires less formula than the previous method developed by {\it G. Adomian} [Nonlinear stochastic operator equations, Academic Press (1986; Zbl 0609.60072)], {\it G. Adomian} and {\it R. Rach} [J. Math. Anal. Appl. 113, 504--509 (1986; Zbl 0617.65046)], {\it G. Adomian}, Applications of nonlinear stochastic systems theory to physics, Kluwer, (1988)]. Many forms of nonlinearity will be studied to illustrate the new algorithm. The new algorithm will be extended to calculate Adomian polynomials for nonlinearity of several variables.

65D20Computation of special functions, construction of tables
Full Text: DOI
[1] Adomian, G.: Nonlinear stochastic operator equations. (1986) · Zbl 0609.60072
[2] Adomian, G.; Rach, R.: On composite nonlinearities and decomposition method. J. math. Anal. appl. 113, 504-509 (1986) · Zbl 0617.65046
[3] Adomian, G.: Applications of nonlinear stochastic systems theory to physics. (1988) · Zbl 0666.60061
[4] Rach, R.: A convenient computational form for the Adomian polynomials. J. math. Anal. appl. 102, 415-419 (1984) · Zbl 0552.60061
[5] Seng, V.; Abbaoui, K.; Cherruault, Y.: Adomian’s polynomials for nonlinear operators. Math. comput. Model. 24, 59-65 (1996) · Zbl 0855.47041
[6] Abbaooui, K.; Cherruault, Y.: Convergence of Adomian’s method applied to differential equations. Comput. math. Appl. 102, 77-86 (1999)
[7] Wazwaz, A. M.: The decomposition method for approximate solution of the Goursat problem. Appl. math. Comput. 69, 299-311 (1995) · Zbl 0826.65077
[8] Wazwaz, A. M.: A new algorithm for calculating Adomian polynomials for nonlinear operators. Appl. math. Comput. 111, 53-69 (2000) · Zbl 1023.65108