Petrov-Galerkin finite element method for solving the MRLW equation

被引：22
|
作者：
Gazi Karakoc S.B. [1 ]
Geyikli T. [2 ]
机构：
[1] Department of Mathematics, Faculty of Science and Art, Nevsehir University, Nevsehir
[2] Department of Mathematics, Faculty of Science and Art, Inonu University, Malatya
来源：
Mathematical Sciences | 2013年 / 7卷 / 1期
关键词：
65D07; 74J35; 74S05; 76B25; Finite element method; MRLW equation; MSC; 65N30; Petrov-Galerkin; Solitary waves; Splines;
D O I：
10.1186/2251-7456-7-25
中图分类号：
学科分类号：
摘要：
Abstract: In this article, a Petrov-Galerkin method, in which the element shape functions are cubic and weight functions are quadratic B-splines, is introduced to solve the modified regularized long wave (MRLW) equation. The solitary wave motion, interaction of two and three solitary waves, and development of the Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracy and efficiency of the method are demonstrated by computing the numerical conserved laws and L2, L∞ error norms. The computed results show that the present scheme is a successful numerical technique for solving the MRLW equation. A linear stability analysis based on the Fourier method is also investigated. © 2013, Karakoc and Geyikli; licensee Springer.
引用
收藏
相关论文
共 50 条
12345