A collocation approach using cubic unified extended trigonometric tension B-splines for solving the time-fractional telegraph equation

Tamsir, Mohammad; Dahman, Neeraj; Nigam, Deependra; Chauhan, Anand; Adel, Waleed

doi:10.22034/cmde.2025.66344.3090

A collocation approach using cubic unified extended trigonometric tension B-splines for solving the time-fractional telegraph equation

Document Type : Research Paper

Authors

¹ Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia.

² Department of Mathematics, Graphic Era Deemed to be University, Dehradun-248002, India.

³ Department of Mathematics, D.A.V. (P.G.) College, Dehradun -248002, India.

⁴ 1. Nanoelectronics Integrated Systems Center, Nile University, Giza, 12588, Egypt. 2. Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Egypt.

10.22034/cmde.2025.66344.3090

Abstract

This paper presents a numerical collocation method based on Cubic Unified Extended Trigonometric Tension B-Spline (CUETTB-spline) functions for solving the Time Fractional Telegraph (TFT) equation. The time-fractional derivative in the TFT equation is discretized using Caputo's definition, followed by the construction of a CUETTB-spline-based collocation method to approximate the solution. The precision and efficiency of the proposed method are demonstrated through three numerical examples, where the results are compared against existing methods for the error norms $L_2$, $L_{\infty}$, and the RMS. The findings reveal that the proposed method achieves higher accuracy than previously reported approaches. Furthermore, a detailed stability analysis confirms that the method is unconditionally stable, while the rate of convergence (ROC) analysis establishes an order of $O(h^2,{\tau }^{2-\alpha })$. The results validate the robustness and effectiveness of the proposed method for solving the time-fractional telegraph equation.

Keywords

Main Subjects

Fractional partial differential equations

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