an:05943924
Zbl 1219.65106
Dehghan, Mehdi; Fakhar-Izadi, Farhad
The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves
EN
Math. Comput. Modelling 53, No. 9-10, 1865-1877 (2011).
00276393
2011
j
65M70 35Q53 76U05 76M25
modified Korteweg-de Vries (mKdV) equation; Ostrovsky equation; collocation method; quartic \(B\)-spline; discrete Fourier series; Chebyshev polynomials
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.