Most results related to discrete nonnegativity conservation principles (DNCP) for elliptic problems are limited to finite differences (FDM) and lowest-order finite element methods (FEM). In this paper we confirm that a straightforward extension to higher-order finite element methods (hpFEM) in the classical sense is not possible. We formulate a weaker DNCP for the Poisson equation in one spatia...

In this paper, we analyze the defect of the rotated 9-point finite difference scheme, and present an optimal 9-point finite difference scheme for the Helmholtz equation with perfectly matched layer (PML) in two dimensional domain. For this method, we give an error analysis for the numerical wavenumber’s approximation of the exact wavenumber. Moreover, based on minimizing the numerical dispersio...

By using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2VBP) withDirichlet, Neumann and Cauchy types boundary conditions. The moment at the knots isapproximated by central finite-difference method. The order of convergence of the methodand the theory is illustrated by solving tes...

The SEIR model for the transmission dynamics of measles is extended by the addition of second-order space derivatives to enable the geographic spread of the disease in a population which has not been vaccinated against it. The resulting system of three reaction-diffusion equations is solved by a convergent finite-difference technique which is second-order accurate in space and time. A parallel ...

This SI contains the finite difference formulation of the ice flow4

In this paper we introduce certain new sequence spaces of fuzzy numbers defined by Iconvergence using sequences of Orlicz functions and a difference operator of orderm. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces. © 2011 Elsevier Ltd. All rights reserved.

Both edge finders use the topological sum to remove noise from second difference responses, so that zero-crossings in these responses represent reliable boundaries. Spectre applies the same techniques to a combination of first and third differences, producing a new map that reliably distinguishes real boundaries from spurious boundaries appearing in staircase intensity patterns. Similar process...

A generalized inverse problem for a two-dimensional difference operator is introduced. Two operators, for which such a problem is solved (we call such operators algebro-geometric), are found.

in this paper we investigate a nonlinear evolution model described by the rosenau-kdv equation. we propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of o(τ2 + h2). furthermore we show the existence and uniqueness of numerical solutions. comparing the numerical results with other methods in...

of the ordinary differential equation which occurs in the boundary condition. An exact nonreflecting boundary condition was derived previously for use with the time dependent wave equation in three Finally, we shall solve a sequence of scattering problems space dimensions. Here it is shown how to combine that boundary by using an explicit finite difference method and our condition with finite d...