in this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. we applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. the main properties of deterministic difference schemes,...

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit original system is obtained, where an extra Gaussian term appears. Such explicitly given in terms of solution Poisson Hilbert space. Moreover, also obtain rate convergence, and convergence shown not to depend on regularity coeffic...

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

We study the diffusion approximation (DA) to the radiative transport equation (RTE) in infinite homogeneous space. Different definitions of the reduced intensity I(r) that satisfy a simplified RTE (without accounting for scattering) and that are often used in the derivation of the DA are examined. By comparing the results of the DA with exact solutions to the RTE, we come to the conclusion that...

Diffusion maps are among the most powerful Machine Learning tools to analyze and work with complex high-dimensional datasets. Unfortunately, the estimation of these maps from a finite sample is known to suffer from the curse of dimensionality. Motivated by other machine learning models for which the existence of structure in the underlying distribution of data can reduce the complexity of estim...