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

Ishtiaq Ali, Hermann Brunner & Tao Tang

DOI:

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 = {}, 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 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 KW - Legendre quadrature formula KW - Pantograph-type delay differential equations KW - Error analysis KW - 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 & Tao Tang. (2019). 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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