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

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_۲, 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^۲,{\tau }^{۲-\alpha }). The results validate the robustness and effectiveness of the proposed method for solving the time-fractional telegraph equation.

کلیدواژه ها:

Caputo TFT equation ، CUETTB-spline functions ، Collocation technique ، Stability analysis ، Convergence