In this paper, we analyze the defect of the rotated 9-point finite difference scheme, and present an optimal 9-point finite difference scheme for the Helmholtz equation with perfectly matched layer (PML) in two dimensional domain. For this method, we give an error analysis for the numerical wavenumber’s approximation of the exact wavenumber. Moreover, based on minimizing the numerical dispersio...

We present a new Vlasov code for collisionless plasmas in the nonrelativistic regime. A Darwin approximation is used for suppressing electromagnetic vacuum modes. The spatial integration is based on an extension of the flux-conservative scheme, introduced by Filbet et al. [F. Filbet, E. Sonnendrücker, P. Bertrand, Conservative numerical schemes for the Vlasov equation, J. Comput. Phys. 172 (200...

An important class of problems exhibits smooth behaviour in space and time on a macroscopic scale, while only a microscopic evolution law is known. For such time-dependent multi-scale problems, an “equationfree framework” has been proposed, of which the gap-tooth scheme is an essential component. The gap-tooth scheme is designed to approximate a time-stepper for an unavailable macroscopic equat...

This study proposes one-dimensional advection diffusion equation (ADE) with finite differences method (FDM) using spreadsheet simulation (ADESS). By changing only the values of weighted parameter with ADESS model, solutions are obtained for the FTSC, Upwind and Lax Wendroff schemes. Two examples which, have the numerical and analytical solutions in literature, are solved in order to test the pr...

in this paper, a chebyshev finite difference method has been proposed in order to solvenonlinear two-point boundary value problems for second order nonlinear differentialequations. a problem arising from chemical reactor theory is then considered. the approachconsists of reducing the problem to a set of algebraic equations. this method can be regardedas a non-uniform finite difference scheme. t...