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.

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...

We compare several local absorbing boundary conditions for solving the Helmholtz equation, by a finite difference or finite element method, exterior to a general scatterer. These boundary conditions are imposed on an artificial elliptical or prolate spheroid outer surface. In order to compare the computational solution with an analytical solution, we consider, as an example, scattering about an...

In this study, a first-order, nonstationary stochastic model of transient flow is developed which is applicable to the entire domain of a bounded vadose zone in the presence of sink/source. We derive general equations governing the statistical moments of the flow quantities by perturbation expansions. Owing to the mathematical complexity of the equations, in general we need to solve them numeri...

The phase error in finite-difference (FD) methods is related to the spatial resolution and thus limits the maximum grid size for a desired accuracy. Greater accuracy is typically achieved by defining finer resolutions or implementing higher order methods. Both these techniques require more memory and longer computation times. In this paper, new modified methods are presented which are optimized...