Applying Multiquadric Quasi-Interpolation to Solve KdV Equation

作     者：Min Lu XIAO Ren Hong WANG Chun Gang ZHU 

作者机构：School of Mathematical Sciences Dalian University of Technology Liaoning 116024 P. R. China 

出 版 物：《Journal of Mathematical Research and Exposition》 (数学研究与评论（英文版）)

年 卷 期：2011年第31卷第2期

页      面：191-201页

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos. 11070131 10801024 U0935004) the Fundamental Research Funds for the Central Universities, China 

主　　题：KdV equation multiquadric(MQ) quasi-interpolation numerical solution 

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 *** 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’ *** this paper,a numerical scheme is presented based on Chen and Wu’s method for solving the Korteweg-de Vries （KdV） *** 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 *** algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid.