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Nonlinear dynamical systems: On the accuracy of Adomian’s decomposition method. (English) Zbl 0719.93041
Summary: This paper deals with the analysis of the time-evolution nonlinear dynamical system modelled by o.d.e. of deterministic type. In particular the convergence and stability of G. Adomian’s solutions [see “Stochastic systems” (1983; Zbl 0523.60056); “Nonlinear stochastic operator equations” (1986; Zbl 0609.60072)] of the problem is investigated. An application is discussed.

MSC:
93C15 Control/observation systems governed by ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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[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] Bonzani, I., On a class of nonlinear stochastich dynamical systems: analysis of the transient behaviour, J. math. anal. appl., 126, 39-50, (1987) · Zbl 0626.60061
[4] Bellomo, N.; de Socio, L., Initial/boundary value problems for the semidiscrete Boltzmann equation: analysis by Adomian’s decomposition method, J. math. anal. appl., 128, 112-124, (1987) · Zbl 0628.45009
[5] Rèpaci, A., Bellman-Adomian solution of nonlinear inverse problem in continuum physics, J. math. anal. appl., 143, 1, 57-65, (1989) · Zbl 0693.35160
[6] Adomian, G., Nonlinear stochastic systems theory and application to physics, (1988), Reidel Dordrecht · Zbl 0666.60061
[7] Bellomo, N., Book review, Foundation of physics, 19, 443-448, (1989)
[8] Cherruault, Y., Convergence of Adomian’s method, Cybernetics, 18, 31-38, (1989) · Zbl 0697.65051
[9] Bellomo, N.; Riganti, R., Nonlinear stochastic systems in physics and mechanics, (1987), World Sci London, New Jersey, Singapore · Zbl 0623.60084
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