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

S. Joe Christin Mary, Sekar Elango (), Muath Awadalla () and Rabab Alzahrani
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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

Mathematics, 2025, vol. 13, issue 11, 1-16

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.

Keywords: Bagley–Torvik equation; Caputo fractional derivative; Robin boundary conditions; minimum principle; finite difference scheme; L 1 scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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