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

被引：1

作者：

Ali, Ishtiaq ^{[1
,2
]}

Brunner, Hermann ^{[3
,4
]}

Tang, Tao ^{[4
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100190, Peoples R China

[2] COMSATS Inst Informat Technol Islamabad, Dept Math, Islamabad, Pakistan

[3] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

[4] Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2009年 / 27卷 / 2-3期

关键词：

Spectral methods; Legendre quadrature formula; Pantograph-type delay differential equations; Error analysis; Exponential convergence; INTEGRAL-EQUATIONS; SUPERCONVERGENCE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 given pantograph delay differential equation are smooth.

引用

页码：254 / 265

页数：12

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