×

zbMATH — the first resource for mathematics

New ideas for proving convergence of decomposition methods. (English) Zbl 0832.47051
Summary: We give new formulae which calculate easily the Adomian’s polynomials used in decomposition methods. Then, the proof of convergence of the Adomian’s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation.

MSC:
47J05 Equations involving nonlinear operators (general)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Adomian, G., Nonlinear stochastic systems theory and applications to physics, (1989), Kluwer, Dordrech Holland · Zbl 0659.93003
[2] K. Abbaoui and Y. Cherruault, Convergence of Adomian’s method applied to differential equations, Mathl. Comput. Modelling\bf28 (5), 103-110. · Zbl 0809.65073
[3] Cherruault, Y., Convergence of Adomian’s method, Kybernetes, 18, 2, 31-38, (1989) · Zbl 0697.65051
[4] Cherruault, Y.; Saccomandi, G.; SomĂ©, B., New results for convergence of Adomian’s method applied to integral equations, Mathl. comput. modelling, 16, 2, 85-93, (1992) · Zbl 0756.65083
[5] Guellal, S.; Cherruault, Y., Practical formulae for calculation of Adomian’s polynomials and application to the convergence of the decomposition method, Int. J. of biomedical comp., 36, 223-228, (1994)
[6] Adomian, G., A review of decomposition method and some recent results for nonlinear equations, Mathl. comput. modelling, 13, 7, 17-43, (1990) · Zbl 0713.65051
[7] Chandrasekharan, K., Arithmetical functions, (1970), Springer-Verlag New York · Zbl 0217.31602
[8] Schwartz, L., Cours d’analyse, (1981), Hermann Paris, France
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.