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Journal of Scientific Computing

Erschienen in:

01.12.2014

Fourier Spectral Methods for Degasperis–Procesi Equation with Discontinuous Solutions

verfasst von: Yinhua Xia

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2014

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Abstract

In this paper, we develop, analyze and test the Fourier spectral methods for solving the Degasperis–Procesi (DP) equation which contains nonlinear high order derivatives, and possibly discontinuous or sharp transition solutions. The \(L^2\) stability is obtained for general numerical solutions of the Fourier Galerkin method and Fourier collocation (pseudospectral) method. By applying the Gegenbauer reconstruction technique as a post-processing method to the Fourier spectral solution, we reduce the oscillations arising from the discontinuity successfully. The numerical simulation results for different types of solutions of the nonlinear DP equation are provided to illustrate the accuracy and capability of the methods.

Vorheriger Artikel A Novel Symmetric Skew-Hamiltonian Isotropic Lanczos Algorithm for Spectral Conformal Parameterizations

Nächster Artikel A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem

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Titel: Fourier Spectral Methods for Degasperis–Procesi Equation with Discontinuous Solutions
verfasst von: Yinhua Xia
Publikationsdatum: 01.12.2014
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2014
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9839-8

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