A numerical approach for a nonhomogeneous differential equation with variable delays

Creative Commons License

Özel M., Tarakçı M., Sezer M.

MATHEMATICAL SCIENCES, cilt.12, sa.2, ss.145-155, 2018 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s40096-018-0253-5
  • Dergi Adı: MATHEMATICAL SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
  • Sayfa Sayıları: ss.145-155
  • Anahtar Kelimeler: Morgan-Voyce polynomials, Matrix method, Collocation method, Delay differential equation, Variable delay, VOLTERRA INTEGRODIFFERENTIAL EQUATIONS, COLLOCATION METHOD, MATRIX-METHOD, DICKSON
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.