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Spectral methods for pantograph-type differential and integral equations with multiple delays |
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| Authors: | Ishtiaq Ali Hermann Brunner Tao Tang |
| Affiliation: | 1. Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China; 2. Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan; 3. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada; 4. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China |
| 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: | Delay differential equation Volterra functional integral equation multiple vanishing delays Legendre spectral method convergence analysis |
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