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...

A finite difference method is developed for solving symmetric positive differential equations in the sense of Friedrichs. The method is applicable to partial differential equations of mixed type with more general boundary conditions. The method is shown to have a convergence rate of 0(hxl2), h being the size of mesh grid. Some numerical results are presented for a model problem of forward-backw...

Direct sinrelations of smalland finite-amplitude disturbances in spatially periodic plane Poiseuille flow were performed. The ability of three high-order finite difference methods to predict the proper behavior of the disturbances was under investigation. The proposed procedure allowed to conclude about the spatial resolution and time-step required bv those schemes to produce numerically accura...

In this paper, Numerical Methods for solving ordinary differential equations, beginning with basic techniques of finite difference methods for linear boundary value problem is investigated. Numerical solution is found for the boundary value problem using finite difference method and the results are compared with analytical solution. MATLAB coding is developed for the finite difference method. T...

A new method combining a finite difference method and a reduced order model (ROM) algorithm is presented for twodimensional (2-D) electromagnetic problems. The problem space is subdivided into subdomains of a generic type. By discretizing the spatial derivatives in a way similar to the finite-difference in time-domain technique (FDTD), the state equations are written down in each subdomain. Fro...

The space and time discretization inherent to all FDTD schemes introduce non-physical dispersion errors, i.e. deviations of the speed of sound from the theoretical value predicted by the governing Euler differential equations. A general methodology for computing this dispersion error via straightforward numerical simulations of the FDTD schemes is presented. The method is shown to provide remar...

In this paper, we present a numerical approach to a class of nonlinear reactiondiffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. ...

We develop a new efficient second-order finite difference scheme for two-dimensional problem of contaminant in groundwater flow. Theoretical analysis shows that the scheme is second-order convergence in the L2 norm and is unconditionally stable. Numerical results demonstrate that the error measures of the second-order scheme are several times smaller than those of the standard implicit finite d...

A conservative three-level linear finite difference scheme for the numerical solution of the initial-boundary value problem of Rosenau-KdV equation is proposed.The difference scheme simulates two conservative quantities of the problemwell.The existence and uniqueness of the difference solution are proved. It is shown that the finite difference scheme is of second-order convergence and unconditi...