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An inventive numerical method for solving the most general form of integro-differential equations with functional delays and characteristic behavior of orthoexponential residual function

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Abstract

In this study, we constitute the most general form of functional integro-differential equations with functional delays. An inventive method based on Dickson polynomials with the parameter-\( \alpha \) along with collocation points is employed to solve them. The stability of the solutions is simulated according to an interval of the parameter-\( \alpha \). A useful computer program is developed to obtain the precise values from the method. The residual error analysis is used to improve the obtained solutions. The characteristic behavior of the residual function is established with the aid of the orthoexponential polynomials. We compare the present numerical results of the method with those obtained by the existing methods in tables.

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Acknowledgements

The authors would like to thank the reviewers for their constructive and valuable comments to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Izmir University of Economics, İzmir, Turkey

    Ömür Kıvanç Kürkçü

  2. Department of Software Engineering, Manisa Celal Bayar University, Manisa, Turkey

    Ersin Aslan

  3. Department of Mathematics, Faculty of Science, Manisa Celal Bayar University, Manisa, Turkey

    Mehmet Sezer

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  1. Ömür Kıvanç Kürkçü
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  2. Ersin Aslan
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  3. Mehmet Sezer
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Correspondence to Ömür Kıvanç Kürkçü.

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Kürkçü, Ö.K., Aslan, E. & Sezer, M. An inventive numerical method for solving the most general form of integro-differential equations with functional delays and characteristic behavior of orthoexponential residual function. Comp. Appl. Math. 38, 34 (2019). https://doi.org/10.1007/s40314-019-0771-2

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  • DOI: https://doi.org/10.1007/s40314-019-0771-2

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