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首页> 外文期刊>Journal of King Saud University >Numerical solution for the Kawahara equation using local RBF-FD meshless method
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Numerical solution for the Kawahara equation using local RBF-FD meshless method

机译：应用局部RBF-FD无网丝法的川马方程式的数值解

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摘要

When the number of nodes increases more than thousands, the arising system of global radial basis functions (RBFs) method becomes dense and ill-conditioned. To solve this difficulty, local RBFs generated finite difference method (RBF-FD) were introduced. RBF-FD method is based on local stencil nodes and so it has a sparsity system. The main goal in this work is to develop the RBF-FD method in order to obtain numerical solution for the Kawahara equation as a time dependent partial differential equation that appears in the shallow water and acoustic waves in plasma. For this purpose, we have discretized the temporal and spatial derivatives with a finite difference,θ-weighted, and RBF-FD methods. Then by applying the collocation technique at the grid nodes, a system of linear equations is obtained which gives the numerical solution of the Kawahara equation. The stability analysis is given. The efficiency and accuracy of the proposed approach are tested by four examples. In addition, a comparison between proposed method and the methods, RBFs, differential quadrature (DQM), cosine expansion based differential quadrature (CDQ) and modified cubic B-Spline differential quadrature (MCBC-DQM) is shown.
机译：当节点数量增加超过数千个时，全局径向基函数（RBFS）方法的产生系统变得密集和不良。为了解决这个困难，引入了本地RBFS产生的有限差分法（RBF-FD）。 RBF-FD方法基于本地模板节点，因此它具有稀疏系统。这项工作中的主要目标是开发RBF-FD方法，以便获得Kawahara方程的数值解决方案，作为在浅水中出现的时间依赖性偏微分方程，其等离子体中的浅水和声波。为此目的，我们已经使时间和空间衍生物离散了具有有限差异，θ加权和RBF-FD方法的时间和空间衍生物。然后，通过在网格节点处应用搭配技术，获得线性方程系统，其给出了川哈拉方程的数值解。给出了稳定性分析。所提出的方法的效率和准确性由四个例子测试。另外，示出了所提出的方法和方法，RBF，差分正交（DQM），余弦扩增基于差分正交（CDQ）和修改立方B样条差分正交（MCBC-DQM）之间的比较。

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