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A Collocation Approach Using Cubic Unified Extended Trigonometric Tension B-Splines for Solving the Time-Fractional Telegraph Equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 مرداد 1404 اصل مقاله (2.5 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.66344.3090 | ||
| نویسندگان | ||
| Mohammad Tamsir1؛ Neeraj Dahman2؛ Deependra Nigam* 3؛ Anand Chauhan2؛ Waleed Adel* 4 | ||
| 1Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia. | ||
| 2Department of Mathematics, Graphic Era Deemed to be University, Dehradun-248002, India. | ||
| 3Department of Mathematics, D.A.V. (P.G.) College, Dehradun -248002, India. | ||
| 4Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Egypt. | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Caputo TFT equation؛ CUETTB-spline functions؛ Collocation technique؛ Stability analysis؛ Convergence | ||
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آمار تعداد مشاهده مقاله: 58 تعداد دریافت فایل اصل مقاله: 126 |
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