On the solution of algebraic equations by the decomposition method. (English) Zbl 0552.60060

Adomian, G.; Rach, R.

J. Math. Anal. Appl. 105, 141-166 (1985).

The decomposition method [the first author, Stochastic Systems (1983; Zbl 0523.60056)] developed to solve nonlinear differential equations has recently been generalized to nonlinear (and/or) stochastic partial differential equations, systems of equations, and delay equations and applied to diverse applications. As pointed out previously (see reference above) the methodology is an operator method which can be used for nondifferential operators as well. Extension has also been made to algebraic equations involving real or complex coefficients. This paper deals specifically with quadratic, cubic, and general higher-order polynomial equations and negative, or nonintegral powers, and random algebraic equations. Further work on this general subject appears in the first author’s book ”Stochastic Systems II,” Academic Press, in press.

MSC:

60H25	Random operators and equations (aspects of stochastic analysis)
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60H15	Stochastic partial differential equations (aspects of stochastic analysis)

Keywords:

decomposition method; operator method; random algebraic equations

Citations:

Zbl 0523.60056

References:

[1]	Adomian, G., Stochastic Systems (1983), Academic Press: Academic Press New York · Zbl 0504.60066
[2]	Bellman, R. E.; Adomian, G., Partial Differential Equations (1984), Reidel: Reidel Dordrecht
[3]	Rach, R., A convenient computational form for the Adomian polynomials, J. Math. Anal. Appl., 102, 415-419 (1984) · Zbl 0552.60061
[4]	Adomian, G., A new approach to nonlinear partial differential equations, J. Math. Anal. Appl., 102, 420-434 (1984) · Zbl 0554.60065
[5]	G. Adomian; G. Adomian · Zbl 0523.60056
[6]	G. Adomian and R. RachJ. Math. Anal. Appl.; G. Adomian and R. RachJ. Math. Anal. Appl. · Zbl 0598.65011
[7]	G. Adomian; G. Adomian · Zbl 0659.93003