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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University, Muğla, Turkey

    Elçin Gökmen

  2. Department of Computer Engineering, Faculty of Engineering and Natural Sciences, Üsküdar University, Istanbul, Turkey

    Burcu Gürbüz

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

    Mehmet Sezer

Authors
  1. Elçin Gökmen
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  2. Burcu Gürbüz
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  3. Mehmet Sezer
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Corresponding author

Correspondence to Burcu Gürbüz.

Additional information

Communicated by Antonio José Silva Neto.

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Gökmen, E., Gürbüz, B. & Sezer, M. A numerical technique for solving functional integro-differential equations having variable bounds. Comp. Appl. Math. 37, 5609–5623 (2018). https://doi.org/10.1007/s40314-018-0653-z

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  • DOI: https://doi.org/10.1007/s40314-018-0653-z

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