We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term by finite difference method. A linear three-level implicit finite difference scheme is designed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is of second-order convergence and unconditionally stable by the discrete energ...

The primary aim of this paper is to answer the question: what are the highest-order fiveor nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the oneand two-dimensional Poisson equation on uniform, quasi-uniform, and non-uniform face-to-face hyper-rectangular grids and directly prove the existence or non-...

A system of coupled singularly perturbed initial value problems with a small parameter is considered. The solution to the system have boundary layers. The structure of these layers is analyzed, and this leads to the construction of a piecewise-uniform Shishkin mesh. On this mesh a hybrid finite difference scheme is proved to be almost second-order accurate, uniformly in the small parameter. Num...

We introduce a simple finite difference scheme for the elliptic interface problem. The scheme is symmetric, definite and monotone with second order accuracy. It is also quite naturally adapted to corner singularities. A simple adaptive strategy yields competitive performance even in the severe case of intersecting interfaces.

The error generated by the classical upwind finite difference method on a uniform mesh, when applied to a class of singularly perturbed model ordinary differential equations with a singularly perturbed Neumann boundary condition, tends to infinity as the singular perturbation parameter tends to zero. Note that the exact solution is uniformly bounded with respect to the perturbation parameter. F...

The error generated by the classical upwind finite difference method on a uniform mesh, when applied to a class of singularly perturbed model ordinary differential equations with a singularly perturbed Neumann boundary condition, tends to infinity as the singular perturbation parameter tends to zero. Note that the exact solution is uniformly bounded with respect to the perturbation parameter. F...

In a fluid-saturated porous medium, an electromagnetic (EM) wavefield induces an acoustic wavefield due to the electrokinetic effect. A potential geophysical application of this effect is electroseismic (ES) logging, in which the converted acoustic wavefield is received in a fluid-filled borehole to evaluate the parameters of the porous formation around the borehole. In this paper, a finite-dif...

in this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (nsfds). numerical examples confirming then efficiency of schemes, for some differential equations are provided. in order toillustrate the accuracy of the new nsfds, the numerical results are compared with s...