Computation of exterior fluid problems often involves solving the Poisson equation in an unbounded domain. To cut down computational cost, it is desirable to minimize the computational domain. Therefore an important numerical issue is how to specify correctly the boundary condition at a finite computational boundary. In this note, we present an efficient method for such a task. The basic idea b...

We consider the reaction-diffusion equation with discontinues coefficients and singular sources in one dimension. In this work, we construct ε-uniformly convergent High Order Compact (HOC) monotone finite difference schemes defined on a priori Shishkin meshes, which have order two, three and four except for a logarithmic factor. Numerical experiments are presented and discussed.

Based on the developed thirdand fourth-order upwind compact finite difference(FD) schemes, a new high-order weighted upwind FD approach, which is called combined compact upwind FD method, is proposed for decreasing dispersive(phase) and dissipative errors of the finite difference approximations. The newly proposed combined compact upwind FD schemes have the characters of group velocity control ...

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, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of tvd (total variation diminishing) of the solution, is proposed. this scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. schemes preserving the essential physical property of tvd are of great importance in practice. such s...