Pell–Lucas series approach for a class of Fredholm-type delay integro-differential equations with variable delays

DÖNMEZ DEMİR D., Lukonde A. P., Kürkçü Ö. K., Sezer M.

Mathematical Sciences, vol.15, no.1, pp.55-64, 2021 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1007/s40096-020-00370-5
  • Journal Name: Mathematical Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.55-64
  • Keywords: Fredholm-type delay integro-differential equations, Matrix-collocation method, Pell–Lucas polynomials and series, Variable delays
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this study, a Pell–Lucas matrix-collocation method is used to solve a class of Fredholm-type delay integro-differential equations with variable delays under initial conditions. The method involves the basic matrix structures gained from the expansions of the functions at collocation points. Therefore, it performs direct and immediate computation. To test its advantage on the applications, some numerical examples are evaluated. These examples show that the method enables highly accurate solutions and approximations. Besides, the accuracy of the solutions and the validity of the method are checked via the residual error analysis and the upper bound error, respectively. Finally, the numerical results, such as errors and computation time, are compared in the tables and figures.