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...

We investigate several existing interface procedures for finite difference methods applied to advection-diffusion problems. The accuracy, stiffness and reflecting properties of the various interface procedures are investigated. The analysis and numerical experiments show that there are only minor differences between the various methods once a proper parameter choice has been made.

To characterise the reflection properties of printed surfaces like FSS (Frequency Selective Surfaces) and EBG (Electromagnetic Band-Gap), it is standard to use a plane wave excitation, and then compare the phase of the incident and the reflected waves. Thus, the phase difference over the frequency can be obtained. Nevertheless, in most cases, only infinite size structures are considered. In thi...

We study a projection and upwind finite difference scheme for a combustion model problem. Convergence to weak solutions is proved under the Courant-Friedrichs-Lewy condition. More assumptions are given on the ignition temperature; then convergence to strong detonation wave solutions or to weak detonation wave solutions is proved.

The large-time behavior of solutions and finite difference approximations of the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance are studied. Asymptotic properties of solutions for the initial-boundary value problem with homogeneous Dirichlet boundary conditions is considered. The rates of convergence are given too. The convergence of...

In order to model the impact of incidents an alternative resolution method is proposed for the Lighthill-Whitham-Richards model. Is is based on an explicit handling of shock waves (generation, tracking and collision). Contrary to finite difference methods which impose a fixed discretization grid, the Wave Tracking method is event based. The different possible events are studied and they all lea...

In this paper we establish the stability condition of a general class of finite difference schemes applied to nonlinear complex reaction-diffusion equations. We consider the numerical solution of both implicit and semi-implicit discretizations. To illustrate the theoretical results we present some numerical examples computed with a semi-implicit scheme applied to a nonlinear equation.

We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H norm are derived. Mathematics Subject Classification. 65N06, 65N12, 65N15, 65N30. Received December 5, 2007. Revised July 21, 2008. Published online December 5, 2008.

This paper describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two-point boundary value problem associated with a fourth order differential equation of the form (py")" + (q r)y 0. Numerical results for two typical eigenvalue problems are tabulated to demonstrate practical usefulness of our methods.

In this paper, we study the behaviour of a microcantilever beam under electrostatic actuation using finite difference method. This problem has a lot of applications in MEMS based devices like accelerometers, switches and others. In this paper, we formulated the problem of a cantilever beam with proof mass at its end and carried out the finite difference solution. we studied the effects of lengt...