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Convergent series solution of nonlinear equations. (English) Zbl 0549.65034
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
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[1] Adomian, G., Stochastic systems, (1983), 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
[3] G. Adomian, A new approach to nonlinear partial differential equations, J. Math. Anal. Appl., to appear. · Zbl 0554.60065
[4] Adomian, G.; Rach, R., Nonlinear stochastic differential delay equations, J. math. anal. appl., 91, 1, 94-101, (1983) · Zbl 0504.60067
[5] G. Adomian and R. Rach, On the solution of algebraic equations by the decomposition method, J. Math. Anal. Appl., to appear. · Zbl 0552.60060
[6] G. Adomian and R. Rach, Application of the decomposition method to inversion of matrices, J. Math. Anal. Appl., to appear. · Zbl 0598.65011
[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
[10] G. Adomian, Applications of Stochastic Systems Theory to Physics and Engineering, to appear. · Zbl 0659.93003
[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 Dordrecht, Holland, to appear
[13] R. Rach, A convenient computational form for the Adomian polynomials, J. Math. Anal. Appl., to appear. · Zbl 0552.60061
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