Spectral methods for pantograph-type differential and integral equations with multiple delays

Ishtiaq Ali; Hermann BRUNNER; Tao TANG

doi:10.1007/s11464-009-0010-z

Spectral methods for pantograph-type differential and integral equations with multiple delays

Ishtiaq Ali^*
, Hermann BRUNNER
, Tao TANG

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

95 Citations (Scopus)

Abstract

We analyze the convergence properties of the spectral method when used to approximate smooth solutions of delay differential or integral equations with two or more vanishing delays. It is shown that for the pantograph-type functional equations the spectral methods yield the familiar exponential order of convergence. Various numerical examples are used to illustrate these results.

Original language	English
Pages (from-to)	49-61
Number of pages	13
Journal	Frontiers of Mathematics in China
Volume	4
Issue number	1
DOIs	https://doi.org/10.1007/s11464-009-0010-z
Publication status	Published - Mar 2009

User-Defined Keywords

Convergence analysis
Delay differential equation
Legendre spectral method
Multiple vanishing delays
Volterra functional integral equation

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10.1007/s11464-009-0010-z

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title = "Spectral methods for pantograph-type differential and integral equations with multiple delays",

abstract = "We analyze the convergence properties of the spectral method when used to approximate smooth solutions of delay differential or integral equations with two or more vanishing delays. It is shown that for the pantograph-type functional equations the spectral methods yield the familiar exponential order of convergence. Various numerical examples are used to illustrate these results.",

keywords = "Convergence analysis, Delay differential equation, Legendre spectral method, Multiple vanishing delays, Volterra functional integral equation",

author = "Ishtiaq Ali and Hermann BRUNNER and Tao TANG",

note = "Funding Information: Acknowledgements The research of Ali and Tang was supported in part by the Hong Kong Research Grants Council and Hong Kong Baptist University. The research of Brunner was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant No. 9406) and Hong Kong Research Grants Council{\textquoteright}s CERG Grant (CERG HKBU 200207). Tang{\textquoteright}s research was also supported by a Joint Research Fund for Hong Kong and Macau Young Scholars awarded by the National Natural Science Foundarion of China.",

year = "2009",

month = mar,

doi = "10.1007/s11464-009-0010-z",

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AU - Ali, Ishtiaq

AU - BRUNNER, Hermann

AU - TANG, Tao

N1 - Funding Information: Acknowledgements The research of Ali and Tang was supported in part by the Hong Kong Research Grants Council and Hong Kong Baptist University. The research of Brunner was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant No. 9406) and Hong Kong Research Grants Council’s CERG Grant (CERG HKBU 200207). Tang’s research was also supported by a Joint Research Fund for Hong Kong and Macau Young Scholars awarded by the National Natural Science Foundarion of China.

PY - 2009/3

Y1 - 2009/3

N2 - We analyze the convergence properties of the spectral method when used to approximate smooth solutions of delay differential or integral equations with two or more vanishing delays. It is shown that for the pantograph-type functional equations the spectral methods yield the familiar exponential order of convergence. Various numerical examples are used to illustrate these results.

AB - We analyze the convergence properties of the spectral method when used to approximate smooth solutions of delay differential or integral equations with two or more vanishing delays. It is shown that for the pantograph-type functional equations the spectral methods yield the familiar exponential order of convergence. Various numerical examples are used to illustrate these results.

KW - Convergence analysis

KW - Delay differential equation

KW - Legendre spectral method

KW - Multiple vanishing delays

KW - Volterra functional integral equation

UR - https://www.scopus.com/pages/publications/60449101518

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DO - 10.1007/s11464-009-0010-z

M3 - Journal article

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SP - 49

EP - 61

JO - Frontiers of Mathematics in China

JF - Frontiers of Mathematics in China

IS - 1

ER -

Spectral methods for pantograph-type differential and integral equations with multiple delays

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