Error Analysis of Generalized LxF Schemes for Linear Advection Equation with Damping

Local oscillations existing in the generalized Lax-Friedrichs (LxF) schemes are proposed and analyzed on computing of the linear advection equation with damping. For the discretization of some special initial data under stable conditions, local oscillations in numerical solutions are observed. Three propositions are also raised about how to control those oscillations via some numerical examples. In order to further explain this, discrete Fourier analysis and the modified equation analysis is used to distinguish the dissipative and dispersive effects of numerical schemes for low frequency and high frequency modes, respectively.

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