求解数值微分问题的广义Hermite谱和拟谱方法  

The generalized Hermite spectral and pseudospectral methods of solving the problem of numerical differentiation

作　　者：冯立新[1] 郭超[1] 

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2017年第4期379-384,共6页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11271113);黑龙江省普通高等学校新世纪优秀人才培养计划资助项目(1253-NECT-019);黑龙江省高等学校科技创新团队基金资助项目(2014TD005)

摘　　要：提出一种基于广义Hermite函数展开的谱方法和拟谱(广义Hermite-Gauss插值)方法,获得相应近似导数的收敛性估计。理论分析表明,此方法有着与ZHAO(2011年)中同样的收敛速度,但通过适当的选取广义Hermite函数中的尺度因子α,可以大大降低投影空间基底的个数,从而提高了计算效率。Spectral and pseudospectral （generalized Hermite-Gauss Interpolation） methods are proposed based on generalized Hermite functions, thereby the convergence estimate of the corresponding approximate derivative is obtained. The theoretical analysis indicates that the proposed methods have the same convergence rates as one in ZHAO＇ s paper （2011）. However, the number of basis functions of the pro- jection space can be significantly reduced by choosing properly the scaling factor c- in generalized Hermite function, thus the computational efficiency of the methods is improved.

关 键 词：数值微分 广义Hermite谱方法 偏差原理 收敛估计 

分 类 号：O241.82[理学—计算数学]