In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger’s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton’s explicit group iterative methods for a general Burger’s equation. The propo...

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...

This paper provides a users’ guide to a new, general finite difference method for the numerical solution of systems of convection dominated conservation laws. We include both extensive motivation for the method design, as well as a detailed formulation suitable for direct implementation. Essentially Non-Oscillatory (ENO) methods are a class of high accuracy, shock capturing numerical methods fo...

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...

Recently, a marching-on in degree finite difference method (MOD-FDM) was employed in the finite-difference time-domain (FDTD) formulation to obtain unconditionally stable transient responses. The objective of this work is to implement a plane wave excitation in the MOD-FDM formulation for scattering problems for an open region. This formulation has volume electric and magnetic current densities...

In this paper, we develop pollution-free finite difference schemes for solving the non-homogeneous Helmholtz equation in one dimension. A family of high-order algorithms is derived by applying the Taylor expansion and imposing the conditions that the resulting finite difference schemes satisfied the original equation and the boundary conditions to certain degrees. The most attractive features o...

in this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. the numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. in order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

The method of difference potentials was originally proposed by Ryaben’kii, and is a generalized discrete version of the method of Calderon’s operators. It handles non-conforming curvilinear boundaries, variable coefficients, and non-standard boundary conditions while keeping the complexity of the solver at the level of a finite-difference scheme on a regular structured grid. Compact finite diff...