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The correct use of the Lax-Friedrichs method. (English) Zbl 1077.65089

The authors analyze the basic phenomena which may arise by the naive use of the Lax-Friedrichs scheme in 1D. They employ a virtually infinite grid, and as a motivation a simple linear model problem is used for their discussion. They also discuss the effects of the discretizations of a finite computational domain with boundary conditions on the numerical solution. A summary of observations and a recipe for the correct application of the Lax-Friedrichs scheme is presented. A nonlinear example is presented to validate the proposed approach and the validity of the investigation in the multi-dimensional case.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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References:

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