Numerical method for a singularly perturbed convection-diffusion problem with delay

Amiraliyev G. M., Çimen E.

APPLIED MATHEMATICS AND COMPUTATION, vol.216, no.8, pp.2351-2359, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 216 Issue: 8
  • Publication Date: 2010
  • Doi Number: 10.1016/j.amc.2010.03.080
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2351-2359
  • Keywords: Singular perturbation, Boundary value problem, Fitted difference method, Delay differential equation, BOUNDARY-VALUE-PROBLEMS, DIFFERENTIAL-DIFFERENCE EQUATIONS, MULTIPLE POSITIVE SOLUTIONS, FINITE-DIFFERENCE, LAYER BEHAVIOR, EXISTENCE
  • Van Yüzüncü Yıl University Affiliated: Yes


This paper deals with the singularly perturbed boundary value problem for a linear second-order delay differential equation. For the numerical solution of this problem, we use an exponentially fitted difference scheme on a uniform mesh which is accomplished by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form. It is shown that one gets first order convergence in the discrete maximum norm, independently of the perturbation parameter. Numerical results are presented which illustrate the theoretical results. (C) 2010 Elsevier Inc. All rights reserved.