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Theoretical analysis of numerical filters. (Chinese. English summary) Zbl 1022.65101

Summary: The analysis, design and modification of the numerical filter method is discussed on the basis of the numerical remainder theory, that is, the dispersive and dissipative effect, especially numerical group velocity. The mechanism of adjusting dispersion and dissipation, and quantitative order of numerical filter are shown for the first time. Numerical tests are obtained by the new method, and the results are satisfactory.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L70 Second-order nonlinear hyperbolic equations
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