二阶奇异摄动问题的新的谱元方法  

New spectral element method for the singular perturbation problem of second order

作　　者：刘志鹏 陶冬亚 LIU Zhipeng;TAO Dongya(School of Economics and Trade,Changzhou Technical Institute of Tourism&Commerce,Changzhou 213032,Jiangsu,China;School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221116,Jiangsu,China)

机构地区：[1]常州旅游商贸高等职业技术学校经济贸易学院,江苏常州213032 [2]江苏师范大学数学与统计学院,江苏徐州221116

出　　处：《上海师范大学学报（自然科学版中英文）》2024年第4期457-464,共8页Journal of Shanghai Normal University(Natural Sciences)

基　　金：国家自然科学基金(11971207)。

摘　　要：由于二阶奇异摄动问题的解具有边界层,用传统的数值方法很难得到理想的逼近效果.为了高效地求解此类问题,对区间做剖分,分别使用移位的映射Legendre多项式和传统Legendre多项式作为基函数,提出新型混合谱元法.该方法能够更好地模拟解在边界层附近的奇异行为.数值结果验证了所提方法的高效性.As the solution of singular perturbation problem of second order has a boundary layer,it is difficult to obtain ideal approximation results for traditional numerical methods.In order to solve these problems efficiently,the interval is divided and a new hybrid spectral element method is proposed by using the shifted mapped Legendre polynomials and the traditional Legendre polynomials as the basis functions.The new method can be used to better simulate the singular behavior of solutions near the boundary layer.Numerical results verify the effectiveness of the proposed method.

关 键 词：谱元法 奇异摄动 映射Legendre多项式 边界层 

分 类 号：O241.82[理学—计算数学]