The solitary wave solution of the two-dimensional regularized long-wave equation in fluids and plasmas

被引:88
作者
Dehghan, Mehdi [1 ]
Salehi, Rezvan [1 ]
机构
[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran 15914, Iran
关键词
Boundary-type meshless methods; Boundary knot method; Analog equation method; Radial basis functions; Solitary waves; Regularized long-wave equation; BOUNDARY KNOT METHOD; PARTIAL-DIFFERENTIAL-EQUATIONS; NUMERICAL-SOLUTION; PSEUDOSPECTRAL METHOD; MODEL-EQUATIONS; GALERKIN METHOD; ELEMENT-METHOD; RLW EQUATION; MESHLESS; SCHEME;
D O I
10.1016/j.cpc.2011.07.018
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
This paper investigates the solitary wave solutions of the two-dimensional regularized long-wave equation which is arising in the investigation of the Rossby waves in rotating flows and the drift waves in plasmas. The main idea behind the numerical solution is to use a combination of boundary knot method and the analog equation method. The boundary knot method is a meshless boundary-type radial basis function collocation technique. In contrast with the method of fundamental solution, the boundary knot method uses the non-singular general solution instead of the singular fundamental solution to obtain the homogeneous solution. Similar to method of fundamental solution, the radial basis function is employed to approximate the particular solution via the dual reciprocity principle. In the current paper, we applied the idea of analog equation method. According to the analog equation method, the nonlinear governing operator is replaced by an equivalent nonhomogeneous linear one with known fundamental solution and under the same boundary conditions. Furthermore, in order to show the efficiency and accuracy of the proposed method, the present work is compared with finite difference scheme. The new method is analyzed for the local truncation error and the conservation properties. The results of several numerical experiments are given for both the single and double-soliton waves. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码:2540 / 2549
页数:10
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