Copyright © 2012 Yeguo Sun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose long-time convergent numerical integration processes for delay differential equations. We first construct an integration process based on modified Laguerre functions. Then we establish its global convergence in certain weighted Sobolev space. The proposed numerical integration processes can also be used for systems of delay differential equations. We also developed a technique for refinement of modified Laguerre-Radau interpolations. Lastly, numerical results demonstrate the spectral accuracy of the proposed method and coincide well with analysis.