解KDV方程的一个二阶三层差分格式  

A Second Order and Tri-level Difference Scheme for KDV Equation

作　　者：李家永[1] 阿不都热西提.阿不都外力 

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《工程数学学报》2007年第6期1137-1140,共4页Chinese Journal of Engineering Mathematics

基　　金：国家自然基金(10571148).

摘　　要：本文讨论KDV方程定界问题的数值解法。对KDV方程构造了一个二阶三层的差分格式,并对非线性项进行了线性化,使格式的近似解更精确。通过严格的误差估计证明了非线性稳定性。数值实验结果表明了理论证明的正确性和格式的有效性。该格式是可行的,有推广价值。In this paper, we discuss the numerical solution of KDV equations. A two-order and three- level difference scheme is constructed for the KDV equation. The approximation solutions are more accurate by transforming the nonlinear term into linear term. The error estimation of the scheme is obtained and the numerical experiment shows the theoretical accuracy and computational effectiveness of the proposed method.

关 键 词：KDV方程 非线性项 非线性稳定性 误差估计 

分 类 号：O241.82[理学—计算数学]