Abstract

In this paper we provide analytical stability estimates for the method of transport We rst prove stability of the second order method of transport ap plied to the linear advection equation with constant coe cient in one dimension by using the von Neumann method and with the positive operator technique In a second step we extend the proof to the linear advection equation with variable coef cient Finally we investigate and compare the existing multidimensional schemes from van Leer Colella and LeVeque for the linear advection equation with constant coe cients

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