On the solution of algebraic equations by the decomposition method.

*(English)*Zbl 0552.60060The 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) |

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\textit{G. Adomian} and \textit{R. Rach}, J. Math. Anal. Appl. 105, 141--166 (1985; Zbl 0552.60060)

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##### References:

[1] | Adomian, G, Stochastic systems, (1983), Academic Press New York · Zbl 0504.60066 |

[2] | Bellman, R.E; Adomian, G, Partial differential equations, (1984), 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] | {\scG. Adomian}, “Stochastic Systems II,” in press. · Zbl 0523.60056 |

[6] | {\scG. Adomian and R. Rach}, Application of the decomposition method to inversion of matrices, J. Math. Anal. Appl., in press. · Zbl 0598.65011 |

[7] | {\scG. Adomian}, “Applications of Stochastic Systems Theory to Physics and Engineering,” to appear. · Zbl 0659.93003 |

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