A numerical technique for solving functional integro-differential equations having variable bounds

Gökmen E., Gürbüz B., Sezer M.

Computational and Applied Mathematics, cilt.37, sa.5, ss.5609-5623, 2018 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 5
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s40314-018-0653-z
  • Dergi Adı: Computational and Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.5609-5623
  • Anahtar Kelimeler: 41A55, 41A58, 65G99, 65L60, Approximate solutions, Collocation points, Functional integro-differential equations, Residual error technique, Taylor polynomials
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this paper, a collocation method based on Taylor polynomials is presented to solve the functional delay integro-differential equations with variable bounds. Using this method, we transform the functional equations to a system of linear algebraic equations. Thus, the unknown coefficients of the approximate solution are determined by solving this system. An error analysis technique based on residual function is developed to improve the numerical solution. Some numerical examples are given to illustrate the accuracy and applicability of the method. Finally, the data are examined according to the residual error estimation. All numerical computations have been performed on the computer programs.