Babolian, E.; Javadi, Sh. New method for calculating Adomian polynomials. (English) Zbl 1055.65068 Appl. Math. Comput. 153, No. 1, 253-259 (2004). The Adomian method is used for solving nonlinear functional equations without discretization or linearization. This technique allows to obtain analytical solutions explicitly depending on time and state variables. The method is based on the calculus of special polynomials (called Adomian polynomials) and the authors give an original technique for obtaining these polynomials in a recurrent and simple way. This involves a routine derivation very similar to those for ordinary functions. Reviewer: Yves Cherruault (Paris) Cited in 30 Documents MSC: 65J15 Numerical solutions to equations with nonlinear operators 47J05 Equations involving nonlinear operators (general) 65Q05 Numerical methods for functional equations (MSC2000) Keywords:Adomian decomposition method; Adomian polynomials; nonlinear functional equations; analytical resolution; recurrent method; Nonlinear operators PDF BibTeX XML Cite \textit{E. Babolian} and \textit{Sh. Javadi}, Appl. Math. Comput. 153, No. 1, 253--259 (2004; Zbl 1055.65068) Full Text: DOI OpenURL References: [1] Adomian, G., Solving frontier problems of physics. the decomposition method, (1994), Kluwer Boston, MA · Zbl 0802.65122 [2] Adomian, G., A review of the decomposition method in applied mathematics, J. math. anal. appl., 135, 501-544, (1988) · Zbl 0671.34053 [3] Abboui, K.; Cherrualt, Y., Convergence of Adomian’s method applied to differential equations, Comput. math. appl., 28, 103-109, (1994) · Zbl 0809.65073 [4] J. Biazar, E. Babolian, A. Nouri, R. Islam, An alternate algorithm for computing Adomian polynomials in special cases, App. Math. Comp., in press · Zbl 1027.65076 [5] Deeba, E.; Khuri, S.A.; Xie, S., An algorithm for solving boundary value problems, J. comput. phys., 159, 125-138, (2000) · Zbl 0959.65091 [6] Wazwaz, A.M., A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. math. comp., 111, 53-69, (2000) · Zbl 1023.65108 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.