Modification and error analysis of an adaptive collocation method for solving delay differential equations

In this paper, we introduce an effective multistep collocation method for solving delay differential equations (DDEs) with constant delays. We determine the convergence properties of the proposed method for delay differential equations with solutions in appropriate Sobolev spaces and show that the proposed scheme enjoys spectral accuracy. Numerical results show that the proposed method can be implemented efficiently and accurately for various DDE model problems.

Keywords:

Delay differential equations , Collocation method , Spectral accuracy , Convergence analysis