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A F ourier pseudospectral method for a generalized improved B oussinesq equation
Author(s) -
Borluk Handan,
Muslu Gulcin M.
Publication year - 2015
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.21928
Subject(s) - gauss pseudospectral method , pseudospectral optimal control , mathematics , convergence (economics) , pseudo spectral method , fourier transform , chebyshev pseudospectral method , mathematical analysis , space (punctuation) , scheme (mathematics) , energy (signal processing) , fourier analysis , computer science , classical orthogonal polynomials , chebyshev equation , economics , orthogonal polynomials , economic growth , statistics , operating system
In this article, we propose a Fourier pseudospectral method for solving the generalized improved Boussinesq equation. We prove the convergence of the semi‐discrete scheme in the energy space. For various power nonlinearities, we consider three test problems concerning the propagation of a single solitary wave, the interaction of two solitary waves and a solution that blows up in finite time. We compare our numerical results with those given in the literature in terms of numerical accuracy. The numerical comparisons show that the Fourier pseudospectral method provides highly accurate results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 995–1008, 2015