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On a class of nonlinear dynamical systems: the structure of a differential operator in the application of the decomposition method. (English) Zbl 0624.34036
Author’s summary: “A suitable expression of a differential operator is deduced, allowing the explicit calculation of the general term \(f_ h\) in the power series expansion of a function f(x,t), to be utilized for solving nonlinear differential equations.”
Reviewer: A.Osborne

37-XX Dynamical systems and ergodic theory
34A34 Nonlinear ordinary differential equations and systems
Full Text: DOI
[1] Adomian, G., Stochastic systems, (1983), Academic Press New York · Zbl 0504.60066
[2] Adomian, G., Nonlinear stochastic operator equations, (1986), Academic Press New York · Zbl 0614.35013
[3] O’Malley, R.E., Introduction to singular perturbations, (1974), Academic Press New York · Zbl 0287.34062
[4] Nayfeh, A.H., ()
[5] Bellomo, N.; Monaco, R., A comparison between Adomian’s decomposition method and perturbation techniques for nonlinear random differential equations, J. math. analysis appl., 110, 495-502, (1985) · Zbl 0575.60064
[6] Adomian, G.; Rach, R., Inversion of nonlinear stochastic operators, J. math. analysis appl., 91, 39-46, (1983) · Zbl 0504.60066
[7] Knuth, D.E., ()
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