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

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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.

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Acknowledgements

The authors would like to thank anonymous reviewers for their constructive and valuable comments, which led to the improvement of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Manisa Celal Bayar University, Manisa, 45140, Turkey

    Duygu Dönmez Demir & Mehmet Sezer

  2. Department of Mathematics, Institute of Natural and Applied Sciences, Manisa Celal Bayar University, Manisa, Turkey

    Alpha Peter Lukonde

  3. Department of Engineering Basic Sciences, Konya Technical University, 42250, Konya, Turkey

    Ömür Kıvanç Kürkçü

Authors
  1. Duygu Dönmez Demir
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  2. Alpha Peter Lukonde
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  3. Ömür Kıvanç Kürkçü
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  4. Mehmet Sezer
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Correspondence to Duygu Dönmez Demir.

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Dönmez Demir, D., Lukonde, A.P., Kürkçü, Ö.K. et al. Pell–Lucas series approach for a class of Fredholm-type delay integro-differential equations with variable delays. Math Sci 15, 55–64 (2021). https://doi.org/10.1007/s40096-020-00370-5

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