A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations


Amiraliyev G., Erdoğan F.

NUMERICAL ALGORITHMS, vol.52, no.4, pp.663-675, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 4
  • Publication Date: 2009
  • Doi Number: 10.1007/s11075-009-9306-z
  • Journal Name: NUMERICAL ALGORITHMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.663-675
  • Erzincan Binali Yildirim University Affiliated: No

Abstract

This study deals with the singularly perturbed initial value problem for a quasilinear first-order delay differential equation. A numerical method is generated on a grid that is constructed adaptively from a knowledge of the exact solution, which involves appropriate piecewise-uniform mesh on each time subinterval. An error analysis shows that the method is first order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. The parameter uniform convergence is confirmed by numerical computations.