and Applied Analysis 3 for λ 2 cos z, where z ∈ : {z : z ∈ , Im z ≥ 0} and αn, Anm are expressed in terms of an and bn as

SEAWAT is a finite-difference computer code designed to simulate coupled variable-density ground water flow and solute transport. This paper describes a new version of SEAWAT that adds the ability to simultaneously model energy and solute transport. This is necessary for simulating the transport of heat and salinity in coastal aquifers for example. This work extends the equation of state for fl...

Let ∆(α) denote the fractional difference operator. In this paper, we define new difference sequence spaces c0(Γ, ∆(α), u) and c(Γ, ∆(α), u). Also, the β−dual of the spaces c0(Γ, ∆(α), u) and c(Γ, ∆(α), u) are determined and calculated their Schauder basis. Furthermore, we characterize the classes (μ(Γ, ∆(α), u) : λ) for μ ∈ {c0, c} and λ ∈ {c0, c, l ∞, l1} .

In the high frequency regime, the geometrical-optics approximation for the Helmholtz equation with a point source results in an eikonal equation for traveltime and a transport equation for amplitude. Because the point-source traveltime field has an upwind singularity at the source point, all formally high-order finite-difference eikonal solvers exhibit first-order convergence and relatively lar...

AD-field is a field with a derivation or a difference-operator, called D. In a suitable language, the theory of D-fields has a modelcompanion, whose axioms need not distinguish the two cases in which D can fall. The geometric concepts involved in describing these axioms can be used to characterize the existentially closed fields with a derivation and a difference-operator; but the class of thes...

We say that a class of finite structures for a finite signature is r-compressible if each structure G in the class has a first-order description of size at most O(r(|G|)). We show that the class of finite simple groups is log-compressible, and the class of all finite groups is log-compressible. The result relies on the classification of finite simple groups, the bi-interpretability of the small...

Abstract. Superconvergence of the velocity is established for mimetic finite difference approximations of second-order elliptic problems over h2-uniform quadrilateral meshes. The superconvergence result holds for a full tensor coefficient. The analysis exploits the relation between mimetic finite differences and mixed finite element methods via a special quadrature rule for computing the scalar...

by, for example, a finite difference method in the computational (μ, χ, φ) space. The above standard dipole coordinates is convenient and certainly appropriate for analytical studies in which the Earth’s dipolar field plays central roles. It also works as a base coordinates for the node and cell generation of the finite element method in the dipole geometry [2, 3]. However, when one tries to us...

We present a finite element analogue to the second-order, finite difference scheme for the solution of the heat diffusion equation in strongly magnetised plasmas given in Günter et al. [S. Günter et al., J. Comp. Phys. 209 (2005) 354]. Compared to standard finite element or finite difference formulations it strongly reduces the pollution of perpendicular heat fluxes by parallel ones even withou...

1 STATEMENT OF THE PROBLEM Our goal is to introduce how derivatives can be approximated by using difference quotients. Suppose we have an interval [a,b] ⊂ R. Let a = x0 < x1 < ·· · < xN−1 < xN = b be a partition. We call {x1, . . . , xN−1} the interior points, and {x0, xN } the boundary. Given a function f : [a,b] → R, we want to approximate the derivative f ′ using our partition. 2 DIFFERENCE ...