This paper contains a numerical analysis of stability, order of accuracy and consistencyof the staggered grid finite difference scheme, used on the elastic wave-equation, as de-scribed by Levander (1988). 1 Finite Difference Analysis1.1 Analysis of Finite Difference SchemesA given partial differential equation can be solved using finite differences. As an example,conside...

We focus on mono-dimensional hyperbolic systems approximated by a particular lattice Boltzmann scheme. The scheme is described in the framework of the multiple relaxation times method and stability conditions are given. An analysis is done to link the scheme with an explicit finite differences approximation of the relaxation method proposed by Jin and Xin. Several numerical illustrations are gi...

A multigrid scheme for the solution of constrained optimal control problems discretized by finite differences is presented. This scheme is based on a new relaxation procedure that satisfies the given constraints pointwise on the computational grid. In applications, the cases of distributed and boundary control problems with box constraints are considered. The efficient and robust computational ...

‎In this paper we propose a numerical scheme to solve the one dimensional nonlinear Klein-Gorden equation‎. ‎We describe the mathematical formulation procedure in details‎. ‎The scheme is three level explicit and based on nonstandard finite difference‎. ‎It has nonlinear denominator function of the step sizes‎. ‎Stability analysis of the method has been given and we prove that the proposed meth...

In this paper we propose a numerical scheme based on finite differences for the numerical solution of nonlinear multi-point boundary value problems over adjacent domains. In each subdomain the solution is governed by different equation. The solutions are required to be smooth across the interfaces. The approach is based on using finite difference approximation of the derivatives at the interfac...

A method is presented for the calculation of in viscid, supercritical flowfields about axisymmetric inlet cowls. A finite-difference calculation is performed in a simple, rectangular domain obtained from the nacelle geometry by a nearly conformal mapping procedure. Type-dependent finite differences are constructed using a coordinate-independent, "rotated" differencing scheme. Methods of acceler...

An industrial scheme, to simulate the two compressible phase flow in porous media, consists in a finite volume method together with a phase-by-phase upstream scheme. The implicit finite volume scheme satisfies industrial constraints of robustness. We show that the proposed scheme satisfy the maximum principle for the saturation, a discrete energy estimate on the pressures and a function of the ...