Klein-Gordon-Zakharov方程初边值问题的Legendre谱方法  

Legendre spectra methods for initial-bounary value problem of Klein-Gordon-Zakharov equations

作　　者：张松山[1] 陈思轶[1] 马和平[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2012年第2期223-238,共16页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11171209);上海市教育委员会重点学科建设资助项目(J50101)

摘　　要：研究Klein-Gordon-Zakharov方程初边值问题的Legendre谱方法.在先验估计的基础上,证明了该格式的稳定性和收敛性,并得到最优阶误差估计.另外,还设计了一个半隐格式,并给出数值例子.在文章的后面给出了多区域谱格式,数值结果表明精度要高于单区域.The Legendre spectral method is proposed for the Klein-Gordon- Zakharov equations with initial boundary conditions. On the basis of a priori estimates, the stability and the convergence of the scheme are proved, and the optimal error estimates are obtained. Besides, a semi-implicit scheme is proposed, and the corresponding numerical examples are given. Moreover, the multidomain Legendre spectral scheme is also constructed, which can be implemented in paral- lel fashion. Finally, numerical results in single domain and multidomain verify the high accuracy of the Legendre spectral method.

关 键 词：Klein—Gordon.Zakharov(KGZ)方程 先验估计 一致收敛 守恒谱格式 多区域 

分 类 号：O241.82[理学—计算数学]