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A numerical approach for a nonhomogeneous differential equation with variable delays

Authors
  • Özel, Mustafa1
  • Tarakçı, Mehmet2
  • Sezer, Mehmet3
  • 1 Dokuz Eylul University, Department of Geophysical Engineering, Faculty of Engineering, Tınaztepe Campus, Buca, İzmir, 35160, Turkey , İzmir (Turkey)
  • 2 Dokuz Eylul University, Department of Physics, Faculty of Science, Tınaztepe Campus, Buca, İzmir, 35160, Turkey , İzmir (Turkey)
  • 3 Celal Bayar University, Department of Mathematics, Faculty of Art and Science, Manisa, Turkey , Manisa (Turkey)
Type
Published Article
Journal
Mathematical Sciences
Publisher
Springer Berlin Heidelberg
Publication Date
Jun 05, 2018
Volume
12
Issue
2
Pages
145–155
Identifiers
DOI: 10.1007/s40096-018-0253-5
Source
Springer Nature
Keywords
License
Green

Abstract

In this study, we consider a linear nonhomogeneous differential equation with variable coefficients and variable delays and present a novel matrix-collocation method based on Morgan–Voyce polynomials to obtain the approximate solutions under the initial conditions. The method reduces the equation with variable delays to a matrix equation with unknown Morgan–Voyce coefficients. Thereby, the solution is obtained in terms of Morgan–Voyce polynomials. In addition, two test problems together with error analysis are performed to illustrate the accuracy and applicability of the method; the obtained results are scrutinized and interpreted by means of tables and figures.

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