substantiation of the averaging method for differential equations with maxima is presented. two theorems on substantiates for differential equations with maxima are established.

Stochastic partial differential equations arise as mathematical models of complex multiscale systems under random influences. Invariant manifolds often provide geometric structure for understanding stochastic dynamics. In this paper, a random invariant manifold reduction principle is proved for a class of stochastic partial differential equations. The dynamical behavior is shown to be described...

In this paper we construct new random walks connected with fractional order differential equations. Namely, the governing equations corresponding to the constructed random walks are multi-term or distributed fractional order differential equations. Nowadays the connection between random walk and fractional order dynamics is well known, see, for instance [1, 17, 26, 33, 38]. A number of construc...

In this note we prove the stochastic homogenization for a large class of fully nonlinear elliptic integro-differential equations in stationary ergodic random environments. Such equations include, but are not limited to Bellman equations and the Isaacs equations for the control and differential games of some pure jump processes in a random, rapidly varying environment. The translation invariant ...

Differential Equations and Stochastic Processes) Limit Theorems for Differential Equations in Random Media by Esteban Alejandro Chávez Casillas Department of Mathematics Duke University

In this paper, for the numerical approximation of random partial differential equations (RPDEs) of parabolic type, an explicit higher order finite difference scheme is constructed. In continuation the main properties of deterministic difference schemes, i.e. consistency, stability and convergency are developed for the random cases. It is shown that the proposed random difference scheme has thes...

In this paper hyperbolic partial differential equations with random coefficients are discussed. We consider the challenging problem of flux functions with coefficients modeled by spatiotemporal random fields. Those fields are given by correlated Gaussian random fields in space and Ornstein–Uhlenbeck processes in time. The resulting system of equations consists of a stochastic differential equat...

Nonlinear Diff. Eqns. Appl. (NoDEA) 10(2003), 431-454. Determining functionals are tools to describe the finite dimensional longterm dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional random dynamical systems. In these applications the convergence condition of the trajectories of an infinite dimensional random dynamical system with ...

in this article differential transformation method (dtms) has been used to solve neutral functional-differential equations with proportional delays. the method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. exact solutions can also be obtained from the kno...

this paper presents a class of theoretical and iterative method for linear partial differential equations. an algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. in this technique, the solution is calculated in the form of a series with easily computable components. there test modeling problems from mathematical mechanic, physi...