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Convergence of a spectral projection of the Camassa‐Holm equation
Author(s) -
Kalisch Henrik,
Raynaud Xavier
Publication year - 2006
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20140
Subject(s) - mathematics , discretization , convergence (economics) , camassa–holm equation , collocation (remote sensing) , spectral method , projection (relational algebra) , partial differential equation , galerkin method , fourier transform , mathematical analysis , algorithm , finite element method , integrable system , computer science , physics , machine learning , economics , thermodynamics , economic growth
A spectral semi‐discretization of the Camassa‐Holm equation is defined. The Fourier‐Galerkin and a de‐aliased Fourier‐collocation method are proved to be spectrally convergent. The proof is supplemented with numerical explorations that illustrate the convergence rates and the use of the dealiasing method. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006