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A comparison between Adomian’s decomposition methods and perturbation techniques for nonlinear random differential equations. (English) Zbl 0575.60064
Comparison of the G. Adomian decomposition method [cf. Stochastic systems. (1983; Zbl 0523.60056)] and regular perturbation techniques applied to the solution of nonlinear vector random differential equations shows that the decomposition method is superior and generally applicable. Even for the cases where perturbation is applicable, the comparison shows that the decomposition method is easier to compute and supplies quantitatively reliable results.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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References:
[1] Adomian, G, Stochastic systems, (1983), Academic Press New York · Zbl 0504.60066
[2] Bellman, R, Methods of nonlinear analysis, (1970), Academic Press New York · Zbl 0204.39901
[3] Soong, T, Random differential equations in science and engineering, (1973), Academic Press New York · Zbl 0348.60081
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