A meshless method using the radial basis functions for numerical solution of the regularized long wave equation
A meshless method using the radial basis functions for numerical solution of the regularized long wave equation
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DOI：
10.1002/num.20457
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发表时间：
2010-07
影响因子：
3.9
通讯作者：
A. Shokri;M. Dehghan
中科院分区：
文献类型：
--
作者：
A. Shokri;M. Dehghan
本文讨论了正则化长波方程的解。正则化长波方程是用来描述波状钻孔的发展过程的，它已被许多科学和工程领域用于建模。提出了一种求解RLW方程的数值方法。该数值模拟的主要思想是利用径向基函数（rbf）进行配置和近似求解。为了避免求解非线性系统，提出了一种预测-校正方案。给出了几个测试问题来验证新技术。数值模拟包括孤立波的传播、两个正孤立波的相互作用、一个正孤立波和一个负孤立波的相互作用、麦克斯韦脉冲转化为稳定孤立波的评价以及波状孔的发展。通过计算运动的三个不变量来确定算法的守恒性质。数值实验结果与解析解和其他最近发表的方法的结果进行了比较，以证实所提出方案的准确性和有效性。©2009 Wiley期刊公司数值方法偏微分方程2010
This article discusses on the solution of the regularized long wave (RLW) equation, which is introduced to describe the development of the undular bore, has been used for modeling in many branches of science and engineering. A numerical method is presented to solve the RLW equation. The main idea behind this numerical simulation is to use the collocation and approximating the solution by radial basis functions (RBFs). To avoid solving the nonlinear system, a predictor‐corrector scheme is proposed. Several test problems are given to validate the new technique. The numerical simulation, includes the propagation of a solitary wave, interaction of two positive solitary waves, interaction of a positive and a negative solitary wave, the evaluation of Maxwellian pulse into stable solitary waves and the development of an undular bore. The three invariants of the motion are calculated to determine the conservation properties of the algorithm. The results of numerical experiments are compared with analytical solution and with those of other recently published methods to confirm the accuracy and efficiency of the presented scheme.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010