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,...

Wedescribe and test an easy-to-implement two-step high-order compact (2SHOC) scheme for the Laplacian operator and its implementation into an explicit finite-difference scheme for simulating the nonlinear Schrödinger equation (NLSE). Our method relies on a compact ‘double-differencing’ which is shown to be computationally equivalent to standard fourthorder non-compact schemes. Through numerical...

Recently the biharmonic form of the Navier-Stokes (N-S) equations have been solved in various domains by using second order compact discretization. In this paper, we present a fourth order essentially compact (4OEC) finite difference scheme for the steady N-S equations in geometries beyond rectangular. As a further advancement to the earlier formulations on the classical biharmonic equation tha...

Convection-diffusion equations are widely used for modeling and simulations of various complex phenomena in science and engineering (Hundsdorfer & Verwer, 2003; Morton, 1996). Since for most application problems it is impossible to solve convection-diffusion equations analytically, efficient numerical algorithms are becoming increasingly important to numerical simulations involving convection-d...

In this paper, we extend a previous work on a compact scheme for the steady Navier Stokes equations [Li, Tang, and Fornberg (1995), Int. J. Numer. Methods Fluids, 20, 1137 1151] to the unsteady case. By exploiting the coupling relation between the streamfunction and vorticity equations, the Navier Stokes equations are discretized in space within a 3_3 stencil such that a fourth order accuracy i...

Abstract This paper aims to developed a high-order and accurate method for the solution of one-dimensional Lotka-Volterra-diffusion with Numman boundary conditions. A fourth-order compact finite difference scheme spatial part combined implicit-explicit Runge Kutta in temporal are proposed. Furthermore, points discretized by using terms fourth order accuracy. key idea proposed is take full advan...

In this paper, we develop a new extrapolation cascadic multigrid (ECMG) method to solve the 3D Poisson equation using the compact finite difference (FD) method. First, a 19-point fourth-order compact difference scheme with unequal meshsizes in different coordinate directions is employed to discretize the 3D Poisson equation on rectangular domains. By combining the Richardson extrapolation and t...

We are concerned with the convergence of Lax-Wendroo type schemes with high resolution to the entropy solutions for conservation laws. These schemes include the original Lax-Wendroo scheme proposed by Lax and Wendroo in 1960 and its two step versions{the Richtmyer scheme and the MacCormack scheme. For the convex scalar conservation laws with algebraic growth ux functions, we prove the convergen...