Difference schemes are treated as operator equations in real linear normed space [l, 23. Twoand three-layer schemes are discussed in real Hilbert space (more precisely, in unitary space, since no use is made of completeness). Stable schemes are classified. Schemes are written in a canonical form that enables stability operators, or what will be termed regularizers, to be introduced. Sufficient ...

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.

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...

A novel spectral-element approach for the eikonal equation is presented based on the work of Tucker et al. This approach is readily implemented in standard finiteelement flow solvers developed for the Navier-Stokes equations. Results are presented for distance function (level set) for three planar configurations: circular cylinder, NACA 0012 airfoil, and T106 airfoil. Results demonstrate that t...

This paper deals with convergence model of interest rates, which explains the evolution of interest rate in connection with the adoption of Euro currency. Its dynamics is described by two stochastic differential equations – the domestic and the European short rate. Bond prices are then solutions to partial differential equations. For the special case with constant volatilities closed form solut...