| MQ拟插值求解KdV方程 |
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| 引用本文： | 肖敏璐,王仁宏,朱春钢.MQ拟插值求解KdV方程[J].数学研究及应用,2011,31(2):191-201. |
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| 作者姓名： | 肖敏璐 王仁宏 朱春钢 |
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| 作者单位： | 大连理工大学数学科学学院, 辽宁 大连 11602;大连理工大学数学科学学院, 辽宁 大连 11602;大连理工大学数学科学学院, 辽宁 大连 11602 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11070131,10801024,U0935004),中央高校基本科研业务费专项基金. |
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| 摘 要： | Quasi-interpolation is very useful in the study of approximation theory and its applications,since it can yield solutions directly without the need to solve any linear system of equations.Based on the good performance,Chen and Wu presented a kind of multiquadric （MQ） quasi-interpolation,which is generalized from the L D operator,and used it to solve hyperbolic conservation laws and Burgers’ equation.In this paper,a numerical scheme is presented based on Chen and Wu’s method for solving the Korteweg-de Vries （KdV） equation.The presented scheme is obtained by using the second-order central divided difference of the spatial derivative to approximate the third-order spatial derivative,and the forward divided difference to approximate the temporal derivative,where the spatial derivative is approximated by the derivative of the generalized L D quasi-interpolation operator.The algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid.
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| 关 键 词： | KdV equation multiquadric（MQ） quasi-interpolation numerical solution |
| 收稿时间： | 2009/6/22 0:00:00 |
| 修稿时间： | 2010/4/26 0:00:00 |
Applying Multiquadric Quasi-Interpolation to Solve KdV Equation |
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| Min Lu XIAO,Ren Hong WANG and Chun Gang ZHU.Applying Multiquadric Quasi-Interpolation to Solve KdV Equation[J].Journal of Mathematical Research with Applications,2011,31(2):191-201. |
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| Authors: | Min Lu XIAO Ren Hong WANG and Chun Gang ZHU |
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| Institution: | School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China |
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| Abstract: | Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations. Based on the good performance, Chen and Wu presented a kind of multiquadric (MQ) quasi-interpolation, which is generalized from the $\mathscr{L_D}$ operator, and used it to solve hyperbolic conservation laws and Burgers' equation. In this paper, a numerical scheme is presented based on Chen and Wu's method for solving the Korteweg-de Vries (KdV) equation. The presented scheme is obtained by using the second-order central divided difference of the spatial derivative to approximate the third-order spatial derivative, and the forward divided difference to approximate the temporal derivative, where the spatial derivative is approximated by the derivative of the generalized $\mathscr{L_D}$ quasi-interpolation operator. The algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid. |
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| Keywords: | KdV equation multiquadric(MQ) quasi-interpolation numerical solution |
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