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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.

65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
Full Text: DOI
[1] Adomian, G.: Nonlinear stochastic systems theory and applications to physics. (1989) · Zbl 0659.93003
[2] Adomian, G.: A review of the decomposition method and some recent results for nonlinear equations. Mathl. comput. Modelling 13, No. 7, 17-43 (1990) · Zbl 0713.65051
[3] Adomian, G.; Rach, R.: Transformation of series. Appl. math. Lett. 4, No. 4, 73-76 (1991) · Zbl 0742.40004
[4] Adomian, G.; Adomian, G. E.: A global method for solution of complex systems. Mathematical modelling 5, No. 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, No. 2, 31-38 (1989) · Zbl 0697.65051
[7] Cherruault, Y.; Saccomandi, G.; Somé, B.: New results for convergence of Adomian’s method applied to integral equations. Mathl. comput. Modelling 16, No. 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)
[10] Rach, R.: A convenient computational form of the Adomian’s plynomials. J. math. Anal. app. 102, 45-419 (1984) · Zbl 0552.60061