A first order convergent numerical method for solving the delay differential problem


Çimen E.

INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, vol.14, no.2, pp.387-402, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2019
  • Journal Name: INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE
  • Journal Indexes: Emerging Sources Citation Index, Scopus
  • Page Numbers: pp.387-402

Abstract

In this paper, the boundary-value problem for a parameter dependent linear first order delay differential equation is analyzed. A finite difference method for approximate solution of this problem is presented. The method is based on fitted difference scheme on a uniform mesh which is achieved by using the method of integral identities which includes the exponential basis functions and applying interpolating quadrature formulas which contain the remainder term in integral form. Also, the method is proved first-order convergent in the discrete maximum norm. Moreover, a numerical example is solved using both the presented method and the Euler method and compared the computed results.