This paper is concerned with transparent boundary conditions for the one dimensional time–dependent Schrödinger equation. They are used to restrict the original PDE problem that is posed on an unbounded domain onto a finite interval in order to make this problem feasible for numerical simulations. The main focus of this article is on the appropriate discretization of such transparent boundary c...

Abstract. An analog of Taylor’s formula, which arises by substituting the classical derivative by a divided difference operator of Askey-Wilson type, is developed here. As an application, a generalization of the binomial theorem is obtained. Besides, this method becomes quite useful to obtain summation formulas of basic hypergeometric series. New proofs of several well-known summation formulas ...

In this work we propose a numerical scheme for a nonlinear and degenerate parabolic problem having application in petroleum reservoir and groundwater aquifer simulation. The degeneracy of the equation includes both locally fast and slow diffusion (i.e. the diffusion coefficients may explode or vanish in some point). The main difficulty is that the true solution is typically lacking in regularit...

Abstract. An analogue of Taylor’s formula, which arises by substituting the classical derivative by a divided difference operator of Askey-Wilson type, is developed here. We study the convergence of the associated Taylor series. Our results complement a recent work by Ismail and Stanton. Quite surprisingly, in some cases the Taylor polynomials converge to a function which differs from the origi...

We consider the Cauchy problem for the Perona-Malik equation ut = div ( ∇u 1 + |∇u|2 ) in a bounded open set Ω ⊆ R, with Neumann boundary conditions. If n = 1, we prove some a priori estimates on u and ux. Then we consider the semi-discrete scheme obtained by replacing the space derivatives by finite differences. Extending the previous estimates to the discrete setting we prove a compactness re...

this paper presents a hybrid method for the optimization of forging process of an aerofoil blade. preform shape and die parting-line angle are optimized in order to minimize the volume of the unfilled die cavity, material waste, forging forces. the overall optimization scheme used in this research work includes a multi-objective approach that is combination of response surface and finite elemen...

a two dimensional generalized thermoelastic problem of a thick circular plate of finite thickness and infinite extent subjected to continuous axisymmetric heat supply and an internal heat generation is studied within the context of generalized thermoelasticity. unified system of equations for classical coupled thermoelasticity, lord-shulman and green-lindsay theory is considered. an exact solut...

two-dimensional euler equations have been solved on an unstructured grid. an upwind finite volume scheme, based on roes flux difference splitting method, is used to discretize the equations. using advancing front method, an initial delaunay triangulation has been made. the adaptation procedure involves mesh enrichment coarsening in regions of flow with high low gradients of flow properties, acc...

A new approach to interpolation theory for functions of several variables is proposed. We develop a multivariate divided difference calculus based on the theory of non-commutative quasi-determinants. In addition, intriguing explicit formulae that connect the classical finite difference interpolation coefficients for univariate curves with multivariate interpolation coefficients for higher dimen...

is finite, and that K(1) = 1, K(2) = 2. For k > 2, Favard gives no quantitative information about K(k). An estimate for the supremum under the additional restriction that only uniform t be considered can be found in Jerome and Schumaker [5]. Their argument was extended by Golomb [4] as far as it will go, viz., to include nonuniform t’s whose global mesh ratio Rt := maxi ∆ti/mini ∆ti is bounded....