In this paper we deal with a model of coupled non-stationary electroelasticity with displacements and potential given on the boundary of a body. We construct a numerical scheme for modeling electromechanical interactions in the body, and present a spectrum of a priori estimates for the solution of this scheme. Such estimates allow us to prove the convergence of the scheme to a generalized solut...

We show that there are simple one dimensional problems for which the MHD code, ZEUS, generates significant errors, whereas upwind conservative schemes perform very well on these problems.

A Measurement Tool to Assess Systematic Reviews (AMSTAR) is a commonly used tool to assess the quality of systematic reviews; however, modifications are needed to improve its usability, reliability, and validity. In this commentary, we summarize our experience and the experiences of others who have used AMSTAR and provide suggestions for its improvement. We propose that AMSTAR should modify a n...

In this paper we consider a class of difference approximations to the Dirichlet problem for second-order elliptic operators with smooth coefficients. The main result is that if the order of accuracy of the approximate problem is v, and F (the right-hand side) and/ (the boundary values) both belong to Cx for X < v, then the rate of convergence is 0(hx).

The numerical solution of the initial value problem for the wave equation is considered for the case when the equation coefficients are piecewise smooth. This problem models linear wave propagation in a medium in which the properties of the medium change discontinuously at interfaces. Convergent difference approximations can be found that do not require the explicit specification of the boundar...

The nonuniform convergence of the Fourier series for discontinuous functions, and in particular the oscillatory behavior of the finite sum, was already analyzed by Wilbraham in 1848. This was later named the Gibbs phenomenon. This article is a review of the Gibbs phenomenon from a different perspective. The Gibbs phenomenon, as we view it, deals with the issue of recovering point values of a fu...

A combined compact difference scheme is proposed for linear second-order partial differential equations with mixed derivative. The scheme is based on a nine-point stencil at interior with sixth-order accurate local truncation error. Fourier analysis is used to analyze the spectral resolution of the proposed scheme. Numerical tests demonstrate at least sixth-order convergence rate with Dirichlet...

The parametric cubic curve is a well-developed subject in the field of computer-aided design. Yet there are still some aspects of its nature that need to be more fully investigated. In this paper, formulations of composite PC curves are presented in an order of increasing rigorousness and order of accuracy. A unique PC curve formulation is developed for the practical use in circle approximation...

In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available. The generalization of compact FD formulas that we propose for scattered nodes and radial basis functions (RBFs) achieves the goal of still keeping the number of stencil ...