非线性演化方程的一个三层差分格式  

A Three-Level Difference Scheme for Nonlinear Evolution Equation

作　　者：李家永[1] 阿布都热西提.阿不都外力 

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）》2007年第3期304-306,共3页Journal of Xinjiang University(Natural Science Edition)

基　　金：国家自然基金(10571148)资助

摘　　要：对非线性演化方程构造了一个三层的差分格式.并对非线性项进行了线性化,使格式的近似解更精确.并且严格估计了误差,证明了非线性稳定性.数值实验表明理论证明的正确性和格式的有效性.In this paper,a two-order and three-level difference scheme is constructed to nonlinear evolution equation. Here the approximation solutions are more accurate by changing the nonlinear term into linear term. The error estimation of the scheme is obtained and the numerical example shows the theoretical accuracy and computational effectiveness of the 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]