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

Çimen E., Amiraliyev G. M.

JOURNAL OF MATHEMATICAL ANALYSIS, cilt.10, sa.3, ss.23-37, 2019 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 3
  • Basım Tarihi: 2019
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.23-37
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.