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


Amiraliyev G. , Erdoğan F.

NUMERICAL ALGORITHMS, cilt.52, ss.663-675, 2009 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 52 Konu: 4
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1007/s11075-009-9306-z
  • Dergi Adı: NUMERICAL ALGORITHMS
  • Sayfa Sayısı: ss.663-675

Özet

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.