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

AMIRALIYEV G. M., 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
  • Van Yüzüncü Yıl University Affiliated: Yes

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

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.