线性变系数中立型变延迟微分方程谱方法的收敛性  

CONVERGENCE OF SPECTRAL METHOD OF LINEAR VARIABLE COEFFICIENT NEUTRAL DIFFERENTIAL EQUATION WITH VARIABLE DELAYS

作　　者：王文强[1] 李东方[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《计算数学》2012年第1期68-80,共13页Mathematica Numerica Sinica

基　　金：国家自然科学基金(11171352;10971175);教育部高校博士点基金(20094301110001);湖南省自科基金(09JJ3002)

摘　　要：本文主要研究了应用谱方法求解线性变系数中立型变延迟微分方程,构造了相应的基于Cheby-shev和Legendre正交多项式的数值方法,证明了其收敛性,最后给出了数值算例.这些结果表明应用谱方法求解延迟微分方程可以获得谱收敛与谱精度的计算效果.This paper mainly studies the application spectral method algorithm for the linear variable neutral delay differential equation with variable coefficient, gives corresponding numerical method based on the Chebyshev and Legendre orthogonal polynomial, prove the convergence, and presents several numerical examples. These results show that application spectrum method for delay differential equations can obtain spectral convergence and spectral precision.

关 键 词：线性中立型变延迟微分方程 谱方法 收敛性 谱精度 谱收敛. 

分 类 号：O175[理学—数学]