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A New Generalized Taylor-Like Explicit Method for Stiff Ordinary Differential Equations

Author

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  • Essam R. El-Zahar

    (Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
    Department of Basic Engineering Science, Faculty of Engineering, Menofia University, Shebin El-Kom 32511, Egypt)

  • José Tenreiro Machado

    (Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal)

  • Abdelhalim Ebaid

    (Department of Mathematics, Faculty of Sciences, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

Abstract

A new generalised Taylor-like explicit method for stiff ordinary differential equations (ODEs) is proposed. The algorithm is presented in its component and vector forms. The error and stability analysis of the method are developed showing that it has an arbitrary high order of convergence and the L-stability property. Moreover, it is verified that several integration schemes are special cases of the new general form. The method is applied on stiff problems and the numerical solutions are compared with those of the classical Taylor-like integration schemes. The results show that the proposed method is accurate and overcomes the shortcoming of the classical Taylor-like schemes in their component and vector forms.

Suggested Citation

  • Essam R. El-Zahar & José Tenreiro Machado & Abdelhalim Ebaid, 2019. "A New Generalized Taylor-Like Explicit Method for Stiff Ordinary Differential Equations," Mathematics, MDPI, vol. 7(12), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1154-:d:292789
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    References listed on IDEAS

    as
    1. Essam R. El-Zahar, 2016. "Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term," International Journal of Differential Equations, Hindawi, vol. 2016, pages 1-12, November.
    2. Amodio, P. & Iavernaro, F. & Mazzia, F. & Mukhametzhanov, M.S. & Sergeyev, Ya.D., 2017. "A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 24-39.
    3. S. A. M. Yatim & Z. B. Ibrahim & K. I. Othman & M. B. Suleiman, 2013. "A Numerical Algorithm for Solving Stiff Ordinary Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-11, February.
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    Cited by:

    1. António M. Lopes & J. A. Tenreiro Machado, 2022. "Nonlinear Dynamics," Mathematics, MDPI, vol. 10(15), pages 1-3, July.

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