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The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves. (English) Zbl 1219.65106
Summary: The Ostrovsky equation (a modified Korteweg-de Vries equation) is used for modeling of a weakly nonlinear surface and internal waves in a rotating ocean. The Ostrovsky equation is a nonlinear partial differential equation and also is complicated due to a nonlinear integral operator as well as spatial and temporal derivatives. We propose a numerical scheme for solving this equation. Our numerical method is based on a collocation method with three different bases such as \(B\)-spline, Fourier and Chebyshev. A numerical comparison of these schemes is also provided by three examples.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
76U05 General theory of rotating fluids
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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