Solvability of forward–backward stochastic di erential equations with nonsmooth coe cients is considered using the Four-Step Scheme and some approximation arguments. For the onedimensional case, the existence of an adapted solution is established for the equation which allows the di usion in the forward equation to be degenerate. As a byproduct, we obtain the existence of a viscosity solution t...

The semi-implicit Euler discretization method is studied for abstract evolution equations in a Hilbert space H, like _ u = f(t; u; u) ; t 2 (0; T ] ; u(0) = u0, where f(t; ; v) is one-sided Lipschitz and R(I hf(t; ; v)) = H for h > 0 su ciently small, and f(t; u; ) is Lipschitz-continuous. Extension to Banach spaces is then pointed out. Ordinary and partial , di erential and integro-di erential...

We present a corrected operator splitting COS method for solving nonlinear parabolic equations of convection di usion type The main feature of this method is the ability to correctly resolve nonlinear shock fronts for large time steps as opposed to standard operator splitting OS which fails to do so COS is based on solving a conservation law for modeling convection a heat type equation for mode...

This work is our rst attempt in establishing the connections between evolutionary computation algorithms and stochastic approximation procedures By treating evo lutionary algorithms as recursive stochastic procedures we study both constant gain and decreasing step size algorithms We formulate the problem in a rather general form supply the su cient conditions for convergence both with probabili...

In the last decades, fractional diierential equations have become more and more popular among scientists and daring engineers in order to model various stable physical phenomena with anomalous decay, say that are not of exponential type. Moreover in discrete-time series analysis, so-called fractional ARMA models have been proposed in the literature in order to model stochastic processes, the au...

In this paper we present an analysis of three di erent formulations of the discontinuous Galerkin method for di usion equations. The rst formulation yields an inconsistent and weakly unstable scheme, while the other two formulations, the local discontinuous Galerkin approach and the Baumann-Oden approach, give stable and convergent results. When written as nite di erence schemes, such a distinc...

In this paper we present an approach for the numerical solution of Delay Di erential Equations y 0 (t) = Ly (t) +My (t ) t 0 y (t) = ' (t) t 0; (1) where > 0, L;M 2 C I m m and ' 2 C ([ ; 0] ; C I m ), di erent from the classical step-by-step method. We restate (1) as an abstract Cauchy problem and then we discretize it in a system of Ordinary Differential Equations. The scheme of discretizatio...

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous ows is obtained by exact integration of the modeled di erential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy e ects...

We present results for numerical simulations of double di usive convection in a rectangular cavity in a variety of situations. The simulations are performed using a streamline-upwind Petrov-Galerkin penalty nite-element method. The uid is modeled as a Boussinesq uid and the Navier Stokes equations are solved in conjunction with the time dependent scalar-convection di usion equations for tempera...

Stability of stochastic di#erential equations with Markovian switching has recently been discussed by many authors, for example, Basak et al. (J. Math. Anal. Appl. 202 (1996) 604), Ji and Chizeck (IEEE Trans. Automat. Control 35 (1990) 777), Mariton (Jump Linear System in Automatic Control, Marcel Dekker, New York), Mao (Stochastic Process. Appl. 79 (1999) 45), Mao et al. (Bernoulli 6 (2000) 73...