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On the Adomian (decomposition) method and comparisons with Picard’s method. (English) Zbl 0645.60067
Summary: This paper shows that the Adomian decomposition method [{\it G. Adomian}, Stochastic systems (1983; Zbl 0523.60056)] is not to be identified with any of the earlier methods since it solves a wide class of nonlinear and stochastic equations without the often unphysical assumptions which have become customary. Similarities between the Picard method and the decomposition method are purely superficial.

60H99Stochastic analysis
Full Text: DOI
[1] Adomian, G.: Stochastic systems. (1983) · Zbl 0523.60056
[2] Adomian, G.: Nonlinear stochastic operator equations. (1986) · Zbl 0609.60072
[3] Adomian, G.: Convergent series solution of nonlinear equations. J. comput. Appl. math. 11, No. No. 2, 225-230 (Oct. 1984) · Zbl 0549.65034
[4] Adomian, G.; Rach, R.: On composite nonlinearities and the decomposition method. J. math. Anal. appl. 113, 504-509 (1986) · Zbl 0617.65046
[5] Adomian, G.; Rach, R.: On the solution of algebraic equations by the decomposition method. J. math. Anal. appl. 105, 141-166 (1985) · Zbl 0552.60060
[6] Adomian, G.; Rach, R.: Algebraic computation and the decomposition method. Kybernetes 15, 33-37 (1986) · Zbl 0604.60064
[7] Adomian, G.: A new approach to nonlinear partial differential equations. J. math. Anal. appl. 102, 420-434 (1984) · Zbl 0554.60065
[8] Adomian, G.: Solution of nonlinear physical problems. Rend. sem. Mat. Torino, 7-22 (1982)
[9] Adomian, G.: Nonlinear stochastic differential equations. J. math. Anal. appl. 55, 441-452 (1976) · Zbl 0351.60053
[10] Adomian, G.: Systems of nonlinear partial differential equations. J. math. Anal. appl. 115, 235-238 (1986) · Zbl 0606.35012
[11] Rach, R.: A convenient computational form for the Adomian polynomials. J. math. Anal. appl. 102, 415-419 (1984) · Zbl 0552.60061
[12] Review, Math. Rev. 84f:60091b.
[13] G. Adomian, ”Applications of Nonlinear Stochastic Theory to Physics,” in press. · Zbl 0659.93003