We establish the global existence of L∞ solutions for a model of polytropic gas flow with diffusive entropy. The result is obtained by showing the convergence of a class of finite difference schemes, which includes the Lax– Friedrichs and Godunov schemes. Such convergence is achieved by proving the estimates required for the application of the compensated compactness theory.

A class of finite difference schemes for solving a fractional anti-diffusive equation, recently proposed by Andrew C. Fowler to describe the dynamics of dunes, is considered. Their linear stability is analyzed using the standard Von Neumann analysis: stability criteria are found and checked numerically. Moreover, we investigate the consistency and convergence of these schemes.

Several numerical schemes utilizing central difference approximations have been developed to solve the Goursat problem. However, in a recent years compact discretization methods which leads to high-order finite difference schemes have been used since it is capable of achieving better accuracy as well as preserving certain features of the equation e.g. linearity. The basic idea of the new scheme...

This article is devoted to the numerical study of various finite difference approximations to the stochastic Burgers equation. Of particular interest in the one-dimensional case is the situation where the driving noise is white both in space and in time. We demonstrate that in this case, different finite difference schemes converge to different limiting processes as the mesh size tends to zero....

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in this paper we define a new labeling called skolem odd difference mean labeling and investigate skolem odd difference meanness of some standard graphs. let g = (v,e) be a graph with p vertices and q edges. g is said be skolem odd difference mean if there exists a function f : v (g) → {0, 1, 2, 3, . . . , p + 3q − 3} satisfying f is 1−1 and the induced map f : e(g) → {1, 3, 5, . . . , 2q−1} d...

(3) (δh[f ])(x) = (∇h 2 [f ])(x)− (∇−h2 [f ])(x). (4) (~ ∆h[r f1 + f2])(n+ 1)(x) = r · (~ ∆h[f1])(n+ 1)(x) + (~ ∆h[f2])(n+ 1)(x). (5) (~ ∆h[f1 + r f2])(n+ 1)(x) = (~ ∆h[f1])(n+ 1)(x) + r · (~ ∆h[f2])(n+ 1)(x). (6) (~ ∆h[r1 f1 − r2 f2])(n+ 1)(x) = r1 · (~ ∆h[f1])(n+ 1)(x)− r2 · (~ ∆h[f2])(n+ 1)(x). (7) (~ ∆h[f ])(1) = ∆h[f ]. (8) (~ ∇h[r f1 + f2])(n+ 1)(x) = r · (~ ∇h[f1])(n+ 1)(x) + (~ ∇h[f2])(...

Taking the axial heat conduction of wax deposition layer into account, a two-dimensional heat transfer model of calculating the temperature profile inside wax deposition layer was deduced and established based on the energy balance equation, the finite difference method was used to solve this model, and the influence of axial heat conduction on the distribution law of temperature profile inside...

A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation. The package provides functions which enable us to solve the determining equations of the related Lie group.

In this article we discuss numerical scheme for the approximation of the Willmore flow of graphs. The scheme is based on the finite difference method. We improve the scheme we presented in [8, 7] which is based on combination of the forward and the backward finite differences. The new scheme approximates the Willmore flow by the central differences and as a result it better preserves symmetry o...