A General Class of Finite-Difference Methods for the Linear Transport Equation

Abstract

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.