Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 15 January 2021Accepted: 02 August 2021Published online: 04 November 2021Keywordsuncertainty propagation, Mellin transform, polynomial chaos expansion, method moments, Gaussian mixture models, unscented transformationAMS Subject Headings34F10, 34C20, 37H10, 60H35, 41A58, ...

We develop a theory of mean-square random invariant manifolds for dynamical systems generated by stochastic differential equations. This is applicable to partial equations driven nonlinear noise. The existence unstable proved the Lyapunov-Perron method based on backward equation involving conditional expectation with respect filtration. stable sets also established but remains open.

In this paper parabolic random partial differential equations and parabolic stochastic partial differential equations driven by a Wiener process are considered. A deterministic, tensorized evolution equation for the second moment and the covariance of the solutions of the parabolic stochastic partial differential equations is derived. Well-posedness of a space-time weak variational formulation ...

differential transform method has been applied to solve many functional equations so far. in this article, we have used this method to solve wave-like equations. differential transform method is capable of reducing the size of computational work. exact solutions can also be achieved by the known forms of the series solutions. some examples are prepared to show theefficiency and simplicity of th...

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