Uniformly convergent numerical method for a singularly perturbed differential difference equation with mixed type

Çimen E.

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, cilt.27, sa.5, ss.755-774, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 5
  • Basım Tarihi: 2020
  • Doi Numarası: 10.36045/j.bbms.200128
  • Dergi Adı: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.755-774
  • Anahtar Kelimeler: Singular perturbation, differential difference equation, fitted difference method, Shishkin mesh, uniform convergence, BOUNDARY-VALUE-PROBLEMS, SMALL SHIFTS, DELAY
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, we deal with the singularly perturbed problem for a linear second order differential difference equation with delay as well as advance. In order to solve the problem numerically, we construct a new difference scheme by the method of integral identities with the use interpolating quadrature rules with remainder terms in integral form. Using an appropriately non-uniform mesh of Shishkin type, we find that the method is almost first order convergent in the discrete maximum norm with respect to the perturbation parameter. Furthermore, we present the numerical experiments that their results support of the theory.