The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves

被引：57

作者：

Dehghan, Mehdi ^{[1
]}

Fakhar-Izadi, Farhad ^{[1
]}

机构：

[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran 15914, Iran

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2011年 / 53卷 / 9-10期

关键词：

Modified Korteweg-de Vries (mKdV) equation; Ostrovsky equation; Collocation method; Quartic B-spline; Discrete Fourier series; Chebyshev polynomials; RADIAL BASIS FUNCTIONS; OSTROVSKY EQUATION; SOLITARY WAVES; NUMERICAL-SOLUTION; GENERALIZED KDV; MKDV EQUATION; TAU METHOD; STABILITY;

D O I：

10.1016/j.mcm.2011.01.011

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Ostrovsky equation (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. In this paper 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. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1865 / 1877

页数：13

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