In this paper, Wong-Zakai approximation methods are presented for some stochastic differential equations in engineering sciences. approximate solutions of the analyzed and numerical results compared with from popular schemes such as Euler-Maruyama Milstein methods. Several problems containing noise investigated examples. Results show that method is a reliable tool studying can be used an altern...

-This paper deals with the adapted Milstein method for solving linear stochastic delay differential equations. It is proved that the numerical method is mean-square (MS) stable under suitable conditions. The obtained result shows that the method preserves the stability property of a class of linear constant-coefficient problems. This is also verified by several numerical examples. (~) 2006 Else...

A unified method for simulating multiphase flows using an exactly mass, momentum, and energy conserving Cell-Integrated SemiLagrangian advection algorithm is presented. The deforming material boundaries are represented using the moment-of-fluid method. The new algorithm uses a semi-implicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection meth...

Semi-Lagrangian (S-L for short) methods, also called quasi-Lagrangian, have been around since the early 1960’s. T.N. Krishnamurti is probably the first to use S-L method. The S-L scheme becomes really popular following Andre Robert’s work in the early 80’s (Robert 1982) when he combined the use of S-L with semi-implicit method (SLSI) which allows for large time step size because both schemes ar...

Based on a group of new Saul’yev type asymmetric difference schemes constructed by author, a high-order, unconditionally stable and parallel alternating segment explicit-implicit method for the numerical solution of the fourth-order heat equation is derived in this paper. The truncation error is fourth-order in space, which is much more accurate than the known alternating segment explicit-impli...

Milstein, Adam B. Ph.D., Purdue University, August, 2004. Imaging of near-infraredfluorescence, absorption, and scatter in turbid media. Major Professor: Charles A.Bouman and Kevin J. Webb.A nonlinear, Bayesian optimization scheme is presented for reconstructing fluo-rescent yield and lifetime, the absorption coefficient, and the diffusion coefficient inturbid media, suc...

we introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition fo...