CONVERGENCE ANALYSIS OF APPROXIMATE METHOD FOR A SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE PROBLEM


Çimen E., Amiraliyev G. M.

JOURNAL OF MATHEMATICAL ANALYSIS, vol.10, no.3, pp.23-37, 2019 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 3
  • Publication Date: 2019
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.23-37
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, we analyze a singularly perturbed convection-diffusion delay problem with Robin condition. In order to solve this problem numerically, we construct a fitted difference scheme on a uniform mesh. The scheme is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. We prove that the method is first order convergence in the discrete maximum norm. Also, we present numerical results that support the theoretical results.