Funaro, Daniele; Pontrelli, Giuseppe A general class of finite-difference methods for the linear transport equation. (English) Zbl 1092.65070 Commun. Math. Sci. 3, No. 3, 403-423 (2005). Summary: A wide family of finite-difference methods for the linear advection equation, based on a six-point stencil, is presented. The family depends on three parameters and includes most of the classical linear schemes. A stability and consistency analysis is carried out. Numerical examples show the performance of the different methods according to the choice of the parameters. The problem of the determination of the parameters providing the “best approximation” is also addressed. Cited in 3 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35L45 Initial value problems for first-order hyperbolic systems 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs Keywords:artificial viscosity; linear advection equation; stability; consistency; Numerical examples PDFBibTeX XMLCite \textit{D. Funaro} and \textit{G. Pontrelli}, Commun. Math. Sci. 3, No. 3, 403--423 (2005; Zbl 1092.65070) Full Text: DOI