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Inversion of nonlinear stochastic operators
Abstract The operator-theoretic method (Adomian and Malakian, J. Math. Anal. Appl. 76(1), (1980), 183–201) recently extended Adomian's solutions of nonlinear stochastic differential equations (G.Expand
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Noise terms in decomposition solution series
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A convenient computational form for the Adomian polynomials
Abstract Recent important generalizations by G. Adomian (“Stochastic Systems”, Academic Press 1983) have extended the scope of his decomposition method for nonlinear stochastic operator equationsExpand
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Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition
Abstract Nonlinear partial differential equations are systematically solved by the decomposition method of G. Adomian for general boundary conditions described by boundary operator equations. LinearExpand
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Modified Adomian Polynomials
A new class of the Adomian Polynomials is defined, which is convenient for computer programming and offers further insights into convergence. This class denoted by A@?"n, as well as the original A"n,Expand
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Generalization of adomian polynomials to functions of several variables
Abstract The solution of nonlinear differential and partial differential equations by the decomposition method due to Adomian [1–3] requires his An polynomials to represent nonlinearities. AExpand
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On the solution of algebraic equations by the decomposition method
Abstract The decomposition method ( G. Adomian, “Stochastic Systems,” Academic Press, New York, 1983 ) developed to solve nonlinear stochastic differential equations has recently been generalized toExpand
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On the analytic solution of the lane-emden equation
The Lane-Emden equation describing temperature in a star in hydrostatic equilibrium was recently solved analytically by N.T. Shawagfeh [1] with highly accurate results using decomposition [1–9].Expand
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Transformation of series
Abstract Nonlinear transformation of series are evaluated using the An polynomials defined in the decomposition method.
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