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Effective numerical technique for solving variable order integro-differential equations

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Abstract

In this article, an effective numerical technique for solving the variable order Fredholm–Volterra integro-differential equations (VO-FV-IDEs), systems of VO-FV-IDEs and variable order Volterra partial integro-differential equations (VO-V-PIDEs) is given. The suggested technique is built on the combination of the spectral collocation method with some types of operational matrices of the variable order fractional differentiation and integration of the shifted fractional Gegenbauer polynomials (SFGPs). The proposed technique reduces the considered problems to systems of algebraic equations that are straightforward to solve. The error bound estimation of using SFGPs is discussed. Finally, the suggested technique’s authenticity and efficacy are tested via presenting several numerical applications. Comparisons between the outcomes achieved by implementing the proposed method with other numerical methods in the existing literature are held, the obtained numerical results of these applications reveal the high precision and performance of the proposed method.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Assuit University, Assuit, 71516, Egypt

    Taha M. El-Gindy

  2. Department of Mathematics, Faculty of Science, Minia University, Minia, 61519, Egypt

    Hoda F. Ahmed

  3. Department of Mathematics, Faculty of Science, New-Valley University, El-Khargah, 72511, Egypt

    Marina B. Melad

Authors
  1. Taha M. El-Gindy
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  2. Hoda F. Ahmed
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  3. Marina B. Melad
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Correspondence to Marina B. Melad.

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El-Gindy, T.M., Ahmed, H.F. & Melad, M.B. Effective numerical technique for solving variable order integro-differential equations. J. Appl. Math. Comput. 68, 2823–2855 (2022). https://doi.org/10.1007/s12190-021-01640-8

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  • DOI: https://doi.org/10.1007/s12190-021-01640-8

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