10.1007/s40096-020-00370-5

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

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  • Duygu Dönmez Demir*1,
  • Alpha Peter Lukonde2,
  • Ömür Kıvanç Kürkçü3,
  • Mehmet Sezer1,
  1. Department of Mathematics, Faculty of Arts and Sciences, Manisa Celal Bayar University, Manisa, 45140, TR
  2. Department of Mathematics, Institute of Natural and Applied Sciences, Manisa Celal Bayar University, Manisa, TR
  3. Department of Engineering Basic Sciences, Konya Technical University, Konya, 42250, TR

Published in Issue 2021-02-08

How to Cite

Dönmez Demir, D., Lukonde, A. P., Kürkçü, Ömür K., & Sezer, M. (2021). Pell–Lucas series approach for a class of Fredholm-type delay integro-differential equations with variable delays. Mathematical Sciences, 15(1 (March 2021). https://doi.org/10.1007/s40096-020-00370-5
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Abstract

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.

Keywords

  • Pell–Lucas polynomials and series,
  • Fredholm-type delay integro-differential equations,
  • Matrix-collocation method,
  • Variable delays

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