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Volume 27, Issue 2-3
A Spectral Method for Pantograph-Type Delay Differential Equations and Its Convergence Analysis

Ishtiaq Ali, Hermann Brunner & Tao Tang

J. Comp. Math., 27 (2009), pp. 254-265.

Published online: 2009-04

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  • Abstract

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.

  • Keywords

Spectral methods, Legendre quadrature formula, Pantograph-type delay differential equations, Error analysis, Exponential convergence.

  • AMS Subject Headings

65M06, 65N12.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-254, author = {Ishtiaq Ali, Hermann Brunner and Tao Tang}, title = {A Spectral Method for Pantograph-Type Delay Differential Equations and Its Convergence Analysis}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {2-3}, pages = {254--265}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8571.html} }
TY - JOUR T1 - A Spectral Method for Pantograph-Type Delay Differential Equations and Its Convergence Analysis AU - Ishtiaq Ali, Hermann Brunner & Tao Tang JO - Journal of Computational Mathematics VL - 2-3 SP - 254 EP - 265 PY - 2009 DA - 2009/04 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8571.html KW - Spectral methods, Legendre quadrature formula, Pantograph-type delay differential equations, Error analysis, Exponential convergence. AB -

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.

Ishtiaq Ali, Hermann Brunner and Tao Tang. (2009). A Spectral Method for Pantograph-Type Delay Differential Equations and Its Convergence Analysis. Journal of Computational Mathematics. 27 (2-3). 254-265. doi:
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