A meshless method of lines for the numerical solution of KdV equation using radial basis functions

被引：44

作者：

Shen, Quan ^{[1
]}

机构：

[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

来源：

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2009年 / 33卷 / 10期

关键词：

Method of lines (MOL); Korteweg-de Vries (KdV); Solitons; Meshless; Radial basis function (RBF); Multiquadric (MQ); Inverse multiquadric(IMQ); Gaussian (GA); BASIS FUNCTION INTERPOLATION; DATA APPROXIMATION SCHEME; MULTIQUADRICS;

D O I：

10.1016/j.enganabound.2009.04.008

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, a meshless method of lines (MOL) is presented for the numerical solution of the Korteweg-de Vries (KdV) equation. This novel method has an advantage over the traditional method of lines which approximates the spatial derivatives using finite difference method (FDM) or finite element method (FEM), because it does not need the mesh in the domain, and it approximates the solution using the radial basis functions (RBFs) on a set of node scattered in problem domain. A comparison among some RBFs is made in numerical examples. Numerical examples demonstrate the accuracy and easy implementation of this novel method and it is an efficient method for the nonlinear time-dependent partial differential equations (PDEs). (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1171 / 1180

页数：10

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