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Compact finite difference schemes with spectral-like resolution. (English) Zbl 0759.65006

Finite difference schemes providing an improved representation of a range of scales ( spectral-like resolution) in the evaluation of derivatives are presented. The errors are considered from the viewpoint of different scales.

[This may partly compensate for the fact that the consideration of the order of the truncation error is not sufficient for the evaluation of the quality of difference schemes when differential equations are to be solved.] On the other hand, stability is not included in the discussion of applications to fluid mechanics.


MSC:
65D25Numerical differentiation
65M06Finite difference methods (IVP of PDE)