A fifth-order nonlinear spectral difference scheme for hyperbolic conservation laws. (English) Zbl 1521.76554
Summary: We develop in this paper a fifth-order nonlinear spectral difference method for solving hyperbolic conservation laws, whose solutions often admit discontinuities. To avoid instability caused by the Gibbs phenomenon arising from interpolation across discontinuities, a fifth-order nonlinear interpolation scheme is proposed within a single cell, keeping the compactness of the original linear spectral difference method. Some numerical results are also presented to demonstrate the accuracy and effectiveness of the proposed method.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
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