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Zbl 1040.60049
El-Tawil, M.; Saleh, M.M.; Elsaidy, M.M.; El-Kalla, I.L.
Decomposition solution of stochastic nonlinear oscillator. (English)
[J] Int. J. Differ. Equ. Appl. 6, No. 4, 411-422 (2002). ISSN 1311-2872

Summary: The decomposition technique of Adomian is applied successfully on stochastic Duf\-fing and Van Der Pol equations, which represent some physical oscillatory systems. The solution process is obtained and then some statistical moments are computed. Comparisons, through figures, are made with some results of {\it M. El-Tawil} and {\it M. Mahmoud} [Mech. Mech. Eng. Int. J. 3, No. 2, 181--188 (1999)], and {\it M. El Tawil} and {\it M. N. Ebady} [Sci. Bull. Fac. Eng. Aain Shams Univ. 33, No. 2, 505--517 (1998)] which use the WHEP technique.

MSC 2000:: *60H10 Stochastic ordinary differential equations

Keywords: Adomian decomposition; Duffing and Van der Pol equations; stochastic processes; statistical moments

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