Trigonometric Cubic B - Spline Collocation Method for Time Fractional Diffusion Equation

Document Type : Research Paper

Authors

Department of Mathematics, National Institute of Technology Calicut, 673601, Kerala, India.

Abstract

This paper presents a numerical approach based on Cubic Trigonometric B-spline (CuTBS) interpolation for solving Time-Fractional Diffusion Equations (TFDEs) involving the Caputo-Fabrizio fractional time derivative. The CuTBS-based scheme effectively combines accurate spatial interpolations with a robust finite difference discretization for the fractional derivative, ensuring high precision in both temporal and spatial domains. The method is unconditionally stable and demonstrates second-order convergence in time and space. Numerical experiments are conducted to validate the applicability and feasibility of the technique.

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Articles in Press, Accepted Manuscript
Available Online from 04 August 2025
  • Receive Date: 18 March 2025
  • Revise Date: 21 July 2025
  • Accept Date: 28 July 2025