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

Delay differential equation / Volterra functional integral equation / multiple vanishing delays / Legendre spectral method / convergence analysis

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