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The long time behavior of a spectral collocation method for delay differential equations of pantograph type

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  • In this paper, we propose an efficient numerical method for delay differential equations with vanishing proportional delay qt (0 < q < 1). The algorithm is a mixture of the Legendre-Gauss collocation method and domain decomposition. It has global convergence and spectral accuracy provided that the data in the given pantograph delay differential equation are sufficiently smooth. Numerical results demonstrate the spectral accuracy of this approach and coincide well with theoretical analysis.
    Mathematics Subject Classification: 34K28, 65L05, 65Q10, 41A10.


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