Convergence of Adomian’s method applied to differential equations. (English) Zbl 0809.65073

The authors present a new proof of the convergence of Adomian’s method applied to differential equations. They give some new formulae and properties and suggest a simple computational form for Adomian’s polynomials.


65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
Full Text: DOI


[1] Adomian, G., Nonlinear stochastic systems theory and applications to physics, (1989), Kluwer · Zbl 0659.93003
[2] Adomian, G., A review of the decomposition method and some recent results for nonlinear equations, Mathl. comput. modelling, 13, 7, 17-43, (1990) · Zbl 0713.65051
[3] Adomian, G.; Rach, R., Transformation of series, Appl. math. lett., 4, 4, 73-76, (1991) · Zbl 0742.40004
[4] Adomian, G.; Adomian, G.E., A global method for solution of complex systems, Mathematical modelling, 5, 4, 251-263, (1984) · Zbl 0556.93005
[5] Adomian, G., On the convergence region for decomposition solution, J. comp. app. math., 11, 379-380, (1984) · Zbl 0547.65053
[6] Cherruault, Y., Convergence of Adomian’s method, Kybernetes, 18, 2, 31-38, (1989) · Zbl 0697.65051
[7] 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
[8] Y. Yang, Convergence of Adomian method and algorithm for Adomian’s polynomials, J. Math. Anal. and Appl. (to appear).
[9] Schwartz, L., Cours d’analyse, (1981), Hermann Paris
[10] Rach, R., A convenient computational form of the Adomian’s plynomials, J. math. anal. app., 102, 45-419, (1984)
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.