Fitted finite difference method for singularly perturbed delay differential equations

Erdoğan F., Amiraliyev G. M.

NUMERICAL ALGORITHMS, vol.59, no.1, pp.131-145, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 1
  • Publication Date: 2012
  • Doi Number: 10.1007/s11075-011-9480-7
  • Journal Name: NUMERICAL ALGORITHMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.131-145
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

This paper deals with singularly perturbed initial value problem for linear second-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first order uniform convergence in the discrete maximum norm. The difference scheme is shown to be uniformly convergent to the continuous solution with respect to the perturbation parameter. A numerical example is solved using the presented method and compared the computed result with exact solution of the problem.

This paper deals with singularly perturbed initial value problem for linear second-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first order uniform convergence in the discrete maximum norm. The difference scheme is shown to be uniformly convergent to the continuous solution with respect to the perturbation parameter. A numerical example is solved using the presented method and compared the computed result with exact solution of the problem.