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A new numerical method for delay and advanced integro-differential equations

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Abstract

A general formulation is constructed for Jacobi operational matrices of integration, product, and delay on an arbitrary interval. The main purpose of this study is to improve Jacobi operational matrices for solving delay or advanced integro–differential equations. Some theorems are established and utilized to reduce the computational costs. All algorithms can be used for both linear and nonlinear Fredholm and Volterra integro-differential equations with delay. An error estimator is introduced to approximate the absolute error when the exact solution of a given problem is not available. The error of the proposed method is less compared to other common methods such as the Taylor collocation, Chebyshev collocation, hybrid Euler–Taylor matrix, and Boubaker collocation methods. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.

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Acknowledgments

The authors are very grateful to the reviewers for carefully reading of the paper and for their comments and suggestions which have improved the paper.

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Authors and Affiliations

  1. Young Researchers and Elite Club, Rasht Branch, Islamic Azad University, Rasht, Iran

    K. Sadri

  2. School of Computing, Engineering and Mathematics, Western Sydney University, Kingswood Campus, Bld Y, Locked bag 1797, Penrith, NSW, 2751, Australia

    A. Amini

  3. Department of Mechanical Engineering, Australian College of Kuwait, Mishref, Kuwait

    A. Amini

  4. Department of Materials Science and Engineering, South University of Science and Technology, Shenzhen, 518055, China

    C. Cheng

  5. Shenzhen Key Laboratory of Nanoimprint Technology, South University of Science and Technology, Shenzhen, 518055, China

    C. Cheng

Authors
  1. K. Sadri
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  2. A. Amini
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  3. C. Cheng
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Correspondence to A. Amini.

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Sadri, K., Amini, A. & Cheng, C. A new numerical method for delay and advanced integro-differential equations. Numer Algor 77, 381–412 (2018). https://doi.org/10.1007/s11075-017-0320-2

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  • DOI: https://doi.org/10.1007/s11075-017-0320-2

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