The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves
The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves
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DOI：
10.1016/j.mcm.2011.01.011
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发表时间：
2011-05
期刊：
影响因子：
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通讯作者：
M. Dehghan;Farhad Fakhar‐Izadi
中科院分区：
文献类型：
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作者：
M. Dehghan;Farhad Fakhar‐Izadi
采用Ostrovsky方程（修正的Korteweg-de弗里斯方程）模拟旋转海洋中弱非线性的表面波和内波。Ostrovsky方程是一个非线性偏微分方程，由于非线性积分算子以及空间和时间导数，也是复杂的。在本文中，我们提出了一个数值方案来解决这个方程。我们的数值方法是基于配点法与三个不同的基地，如B样条，傅立叶和切比雪夫。通过三个算例对这些格式进行了数值比较。
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.