A class of generalized high order finite compact difference schemes is proposed for shock/vortex, shock/boundary layer interaction problems. The finite compact difference scheme takes the region between two shocks as a compact stencil. The high order WENO fluxes on shock stencils are used as the internal boundary fluxes for the compact scheme. A lemma of the property of smoothness estimators on...

We present a two level nite di erence scheme for the approximation of nonlinear parabolic equations. Discrete inner products and the lowest order Raviart-Thomas approximating space are used in the expanded mixed method in order to develop the nite di erence scheme. Analysis of the scheme is given assuming an implicit time discretization. In this two level scheme, the full nonlinear problem is s...

We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general H1 initial data and thus peakon-antipeakon interactions. Assuming a specified condition restricting the time step in terms of the spatial discretization parameter, we prove that the difference scheme converges strongly in H1 towards a dissipative weak solution of C...

A new discretization scheme for partial differential equations, based on the finite differences method, and its application to the two dimensional static diffusion equation is presented. This scheme produces better approximations than a standard use of finite differences. It satisfies properties of continuous differential operators and discrete versions of integral identities, which guarantee i...

This paper includes two parts. In the first part, general error estimates for "stable" eigenvalue approximations are obtained. These are practical in the sense that they are based on the discretization error of the difference formula over the eigenspace associated with the isolated eigenvalue under consideration. Verification of these general estimates are carried out on two difference schemes:...

We introduce the standard fourth order compact finite difference formulae. We show how these formulae apply in the special case of the heat equation. It is well known that the American option pricing problem may be formulated in terms of the Black Scholes partial differential equation (PDE) together with a free boundary condition. Standard methods allow this problem to be transformed into a mov...

Level set methods [Osher and Sethian. Fronts propagating with curvaturedependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79 (1988) 12] have proved very successful for interface tracking in many different areas of computational science. However, current level set methods are limited by a poor balance between computational efficiency and storage requirements. Tre...

One of the more interesting themes of the mathematical ecology is the description of the mutualistic interaction between two interacting species. Based on continuous-time model developed by Holland and DeAngelis 2009 for consumer-resource mutualism description, this work deals with the application of the Mickens Non Standard Finite Difference method to transform the continuous-time scheme into ...

We use equations similar to the heat conduction equation to calulate heat transfer, radiation transfer and hydrostatical equilibrium in our stellar evolution programs. We tried various numerical schemes and found that the most convenient scheme for complicated calculations (nonlinear, multidimensional calculations) is a symmetrical semi-implicit (SSI) scheme. The (SSI) scheme is easy to code, v...

In this paper, a room acoustics simulation using a finite difference approximation on a face-centered cubic (FCC) grid with finite volume impedance boundary conditions is presented. The finite difference scheme is accelerated on an Nvidia Tesla K20 graphics processing unit (GPU) using the CUDA programming language. A performance comparison is made between 27-point finite difference schemes on a...