This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations multiplicative noise. A prototypical method, which comprises Euler–Maruyama scheme for time discretization and Taylor-Hood spatial studied in detail. Strong convergence rates established not only velocity approximation but also pressure (in a time-averaged fashion). ...

We combine a discrete-element-method simulation with a stochastic process to model the movement of spherical particles in a turbulent channel flow. With this model we investigate the mixing properties of two species of particles flowing through the channel. We find a linear increase of the mixing zone with the length of the pipe. Flows at different Reynolds number are studied. Below a critical ...

We consider the numerical solution of the steady-state Navier–Stokes equations with uncertain data. Specifically, we treat the case of uncertain viscosity, which results in a flow with an uncertain Reynolds number. After linearization, we apply a stochastic Galerkin finite element method, combining standard inf-sup stable Taylor–Hood approximation on the spatial domain (on highly stretched grid...

in this paper, we apply the differential transform (dt) method for finding approximate solution of the system of linear and nonlinear volterra integro-differential equations with variable coefficients, especially of higher order. we also obtain an error bound for the approximate solution. since, in this method the coefficients of taylor series expansion of solution is obtained by a recurrence r...

We are concerned with the stochastic differential delay equations with Poisson jump and Markovian switching SDDEsPJMSs . Most SDDEsPJMSs cannot be solved explicitly as stochastic differential equations. Therefore, numerical solutions have become an important issue in the study of SDDEsPJMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions a...

We apply improved Taylor expansion method which is one of the variational schemes to Ising model in two-dimensions. It enables us to evaluate free energy and magnetization at strong coupling regions from weak coupling expansion even in the presence of the phase transition. We determine approximated transition point in this scheme. In the presence of external magnetic field we can see not only s...

In this paper we study the pricing of exchange options between two underlying assets whose dynamic show a stochastic correlation with random jumps. particular, consider Ornstein-Uhlenbeck covariance model, Levy Background Noise Processes driven by Inverse Gaussian subordinators. We use expansions in terms Taylor polynomials and cubic splines to approximately compute price derivative contract. O...

The subject of this paper is an analytic approximate method for a class stochastic differential equations with coefficients that do not necessarily satisfy the Lipschitz and linear growth conditions but behave like polynomials. More precisely, from observed have unique solutions bounded moments their polynomial condition. Approximate are defined on partitions time interval, Taylor approximation...

Linear-implicit versions of strong Taylor numerical schemes for finite dimensional It6 stochastic differential equations (SDEs) are shown to have the same order as the original scheme. The combined truncation and global discretization error of an 7 strong linear-implicit Taylor scheme with time-step A applied to the N dimensional It6-Galerkin SDE for a class of parabolic stochastic partial diff...

In this paper an efficient, simulation-based, maximum likelihood (ML) method is proposed for estimating Taylor’s stochastic volatility (SV) model. The new method is based on the second order Taylor approximation to the integrand. The approximation enables us to transfer the numerical problem in the Laplace approximation and that in importance sampling into the problem of inverting two high dime...