Convergent series solution of nonlinear equations. (English) Zbl 0549.65034

Adomian, G.

J. Comput. Appl. Math. 11, 225-230 (1984).

In previous papers, computational procedures for solving large class of nonlinear (and/or stochastic) equations were provided by the author’s decomposition method. In the present work some important properties of the author’s finite set \(A_ n\) of polynomials in terms of which the nonlinearities can be expressed are shown, ensuring an accurate and computable convergent solution by the decomposition method.

Reviewer: L.Vulkov

MSC:

65J15

Numerical solutions to equations with nonlinear operators

Keywords:

convergent series solution; stochastic equations; decomposition method; computable convergent solution

References:

[1]	Adomian, G., Stochastic Systems (1983), Academic Press: Academic Press New York · Zbl 0504.60066
[2]	Adomian, G., On product nonlinearities in stochastic differential equations, Appl. Math. Comput., 8, 1 (1981) · Zbl 0454.60060
[4]	Adomian, G.; Rach, R., Nonlinear stochastic differential delay equations, J. Math. Anal. Appl., 91, 1, 94-101 (1983) · Zbl 0504.60067
[7]	Adomian, G., Stochastic nonlinear modeling of fluctuations in a nuclear reactor—a new approach, Ann. Nuclear Energy, 8, 329-330 (1981)
[8]	Adomian, G.; Sibul, L., On the control of stochastic systems, J. Math. Anal. Appl., 83, 2, 611-621 (1981) · Zbl 0476.93077
[9]	Adomian, G., Stabilization of a stochastic nonlinear economy, J. Math. Anal. Appl., 88, 1, 306-317 (1982) · Zbl 0483.90025
[11]	Adomian, G.; Rach, R., Inversion of nonlinear stochastic operators, J. Math. Anal. Appl., 91, 1, 39-46 (1983) · Zbl 0504.60066
[12]	Bellman, R. E.; Adomian, G., Nonlinear Partial Differential Equations (1983), Reidel: Reidel Dordrecht, Holland, to appear