A numerical approach for a nonhomogeneous differential equation with variable delays


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Özel M., Tarakçı M., Sezer M.

MATHEMATICAL SCIENCES, vol.12, no.2, pp.145-155, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1007/s40096-018-0253-5
  • Journal Name: MATHEMATICAL SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.145-155
  • Keywords: Morgan-Voyce polynomials, Matrix method, Collocation method, Delay differential equation, Variable delay, VOLTERRA INTEGRODIFFERENTIAL EQUATIONS, COLLOCATION METHOD, MATRIX-METHOD, DICKSON
  • Dokuz Eylül University Affiliated: Yes

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.