::title::Convergence Analysis of Spectral Methods for Integro-Differential Equations with Vanishing Proportional Delays 
::author::1::Ishtiaq Ali
::address::1::Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, 44000, Islamabad, Pakistan
::email::ishtiaqali@comsats.edu.pk
::receive::Received 2009-6-26 Accepted 2010-1-13
::online::Available online 2010-9-20
::DOI::10.4208/jcm.1004-m3150
::keywords::Delay integro-differential equations, Proportional delays, Spectral methods, Convergence analysis.
::ams::65R20, 34K28.
::abstract::
We describe the application of the spectral method to delay integro-differential 
equations with proportional delays. It is shown that the resulting numerical 
solutions exhibit the spectral convergence order. Extensions to equations with 
more general (nonlinear) vanishing delays are also discussed.