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An Efficient Numerical Method for the Fractional Bagley–Torvik Equation of Variable Coefficients with Robin Boundary Conditions

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Listed:
  • S. Joe Christin Mary

    (Temporary Faculty, Department of Mathematics, National Institute of Technology, Tiruchirappalli 620015, Tamil Nadu, India)

  • Sekar Elango

    (Department of Mathematics, Amrita School of Physical Science, Amrita Vishwa Vidyapeetham, Coimbatore 641112, Tamil Nadu, India)

  • Muath Awadalla

    (Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia)

  • Rabab Alzahrani

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia)

Abstract

In this paper, we propose a numerical method for the fractional Bagley–Torvik equation of variable coefficients with Robin boundary conditions. The problem is approximated using a finite difference scheme on a uniform mesh that combines the L1 scheme with central differences. We prove that this numerical method is almost first-order convergent. The error bounds for the numerical approximation are derived. The numerical calculations carried out for the given examples validate the theoretical results.

Suggested Citation

  • S. Joe Christin Mary & Sekar Elango & Muath Awadalla & Rabab Alzahrani, 2025. "An Efficient Numerical Method for the Fractional Bagley–Torvik Equation of Variable Coefficients with Robin Boundary Conditions," Mathematics, MDPI, vol. 13(11), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1899-:d:1672916
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    References listed on IDEAS

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    1. Karaaslan, Mehmet Fatih & Celiker, Fatih & Kurulay, Muhammet, 2016. "Approximate solution of the Bagley–Torvik equation by hybridizable discontinuous Galerkin methods," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 51-58.
    2. Sekar Elango & Lolugu Govindarao & Muath Awadalla & Hajer Zaway, 2025. "Efficient Numerical Methods for Reaction–Diffusion Problems Governed by Singularly Perturbed Fredholm Integro-Differential Equations," Mathematics, MDPI, vol. 13(9), pages 1-14, May.
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