Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators

• We construct accurate central difference stencils for problems involving high frequency waves or multi-frequency solutions over long time intervals with a relatively coarse spatial mesh, and with an easily obtained bound on the dispersion error. This is done by demonstrating that the problem of constructing central difference stencils that have minimal dispersion error in the infinity norm can be recast into a problem of approximating a continuous function from a finite dimensional subspace with a basis forming a Chebyshev set. In this new formulation, characterising and numerically obtaining optimised schemes can be done using established theory.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Dispersion relation; Wave propagation; Wavenumber approximation; Finite differences; Approximation theory

Publication and Content Type

ref (subject category)

art (subject category)