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An assessment of spectral nonoscillatory schemes. (English) Zbl 0811.65081

The performance of the spectral essentially nonoscillatory (ENO) scheme of W. Cai and C.-W. Shu [J. Comput. Phys. 104, No. 2, 427-443 (1993; Zbl 0766.76069)] on the approximation of a periodic function with smooth structure and several discontinuities is assessed. Then, a new spectral ENO interpolation scheme that achieves spectral accuracy in smooth regions and is nonoscillatory on piecewise discontinuous data is proposed. The basic idea is to increase the order of the ENO scheme in proportion to the number of points wherever possible.
Numerical experiments with the new scheme on interpolation, 1D advection, inviscid Burgers’ equation and 1D gas dynamics confirm the high resolution features of the scheme. Comparisons with the results of earlier spectral nonoscillatory schemes show that the new one is competitive both in efficiency and accuracy.
Reviewer: K.Zlateva (Russe)

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65D05 Numerical interpolation
35Q53 KdV equations (Korteweg-de Vries equations)
76N15 Gas dynamics (general theory)
35L60 First-order nonlinear hyperbolic equations

Citations:

Zbl 0766.76069
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References:

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