A SPECTRAL METHOD FOR PANTOGRAPH-TYPE DELAY DIFFERENTIAL EQUATIONS AND ITS CONVERGENCE ANALYSIS  

作　　者：Ishtiaq Ali Hermann Brunner 

机构地区：[1]Institute of Computational Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]Department of Mathematics,COMSA TS Institute of Information Technology Islamabad,Pakistan [3]Hermann Brunner Department of Mathematics and Statistics,Memorial University of Newfoundland,St.John’s,Canada [4]Department of Mathematics,Hong Kong Baptist University,Hong Kong,China

出　　处：《Journal of Computational Mathematics》2009年第2期254-265,共12页计算数学（英文）

基　　金：The research of HB was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada and by the Research Grants Council of Hong Kong;The research of TT was supported by Hong Kong Baptist University,the Research Grants Council of Hong Kong and he was supported in part by the Chinese Academy of Sciences while visiting its Institute of Computational Mathematics.

摘　　要：We propose a novel numerical approach for delay differential equations with vanishing proportional delays based on spectral methods. A Legendre-collocation method is employed to obtain highly accurate numerical approximations to the exact solution. It is proved theoretically and demonstrated numerically that the proposed method converges exponentially provided that the data in the are smooth. given pantograph delay differential equationWe propose a novel numerical approach for delay differential equations with vanishing proportional delays based on spectral methods. A Legendre-collocation method is employed to obtain highly accurate numerical approximations to the exact solution. It is proved theoretically and demonstrated numerically that the proposed method converges exponentially provided that the data in the are smooth. given pantograph delay differential equation

关 键 词：Spectral methods Legendre quadrature formula Pantograph-type delay differential equations Error analysis Exponential convergence 

分 类 号：O241.82[理学—计算数学]