A singularly perturbed differential equation with piecewise constant argument of generalized type

AKHMET M., Dauylbayev M., Mirzakulova A.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.4, pp.1680-1685, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1704-19
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1680-1685
  • Keywords: Piecewise constant argument of generalized type, small parameter, singular perturbation, approximate solution, humping in the boundary layer area
  • Middle East Technical University Affiliated: Yes

Abstract

The paper considers the extension of Tikhonov Theorem for singularly perturbed differential equation with piecewise constant argument of generalized type. An approximate solution of the problem has been obtained. A new phenomenon of humping has been observed in the boundary layer area. An illustrative example with simulations is provided.