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Numerical algorithm for solving multi-pantograph delay equations on the half-line using Jacobi rational functions with convergence analysis

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Abstract

A new spectral Jacobi rational-Gauss collocation (JRC) method is proposed for solving the multi-pantograph delay differential equations on the half-line. The method is based on Jacobi rational functions and Gauss quadrature integration formula. The main idea for obtaining a semi-analytical solution for these equations is essentially developed by reducing the pantograph equations with their initial conditions to systems of algebraic equations in the unknown expansion coefficients. The convergence analysis of the method is analyzed. The method possesses the spectral accuracy. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. Indeed, the present method is compared favorably with other methods.

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Acknowledgements

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

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

    Eid H. Doha

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    Ali H. Bhrawy

  3. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    Ali H. Bhrawy

  4. Department of Mathematics, Alwagjh University College, University of Tabuk, Tabuk, Saudi Arabia

    Ramy M. Hafez

  5. Department of Basic Science, Institute of Information Technology, Modern Academy, Cairo, Egypt

    Ramy M. Hafez

Authors
  1. Eid H. Doha
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  2. Ali H. Bhrawy
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  3. Ramy M. Hafez
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Corresponding author

Correspondence to Ali H. Bhrawy.

Additional information

Supported in part by the National Natural Science Foundation of China under Grant No. 11021161 and 10928102, 973 Program of China under Grant No. 2011CB80800, Chinese Academy of Sciences under Grant No. kjcx-yw-s7, project grant of “Center for Research and Applications in Plasma Physics and Pulsed Power Technology, PBCT-Chile-ACT 26” and Direcci´on de Programas de Investigaci´on, Universidad de Talca, Chile.

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Doha, E.H., Bhrawy, A.H. & Hafez, R.M. Numerical algorithm for solving multi-pantograph delay equations on the half-line using Jacobi rational functions with convergence analysis. Acta Math. Appl. Sin. Engl. Ser. 33, 297–310 (2017). https://doi.org/10.1007/s10255-017-0660-7

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  • DOI: https://doi.org/10.1007/s10255-017-0660-7

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