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Tamsir, Mohammad, Dahman, Neeraj, Nigam, Deependra, Chauhan, Anand, Adel, Waleed. (1405). A collocation approach using cubic unified extended trigonometric tension B-splines for solving the time-fractional telegraph equation. سامانه مدیریت نشریات علمی, 14(4), 1576-1594. doi: 10.22034/cmde.2025.66344.3090
Mohammad Tamsir; Neeraj Dahman; Deependra Nigam; Anand Chauhan; Waleed Adel. "A collocation approach using cubic unified extended trigonometric tension B-splines for solving the time-fractional telegraph equation". سامانه مدیریت نشریات علمی, 14, 4, 1405, 1576-1594. doi: 10.22034/cmde.2025.66344.3090
Tamsir, Mohammad, Dahman, Neeraj, Nigam, Deependra, Chauhan, Anand, Adel, Waleed. (1405). 'A collocation approach using cubic unified extended trigonometric tension B-splines for solving the time-fractional telegraph equation', سامانه مدیریت نشریات علمی, 14(4), pp. 1576-1594. doi: 10.22034/cmde.2025.66344.3090
Tamsir, Mohammad, Dahman, Neeraj, Nigam, Deependra, Chauhan, Anand, Adel, Waleed. A collocation approach using cubic unified extended trigonometric tension B-splines for solving the time-fractional telegraph equation. سامانه مدیریت نشریات علمی, 1405; 14(4): 1576-1594. 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

Computational Methods for Differential Equations
مقاله 4، دوره 14، شماره 4، دی 2026، صفحه 1576-1594    اصل مقاله (1.73 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.
41. Nanoelectronics Integrated Systems Center, Nile University, Giza, 12588, Egypt. 2. Department 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
مراجع
  • [1] O. F. Azhar, F. Naeem, F. Mofarreh, and J. Kaflem, Numerical analysis of the fractional-order telegraph equations, J. Func. Spac., 2021 (2021), 1–14.
  • [2] Z. Abdollahy, Y. Mahmoudi, A. Salimi Shamloo, and M. Baghmisheh, Haar Wavelets method for time-fractional Riesz space telegraph equation with separable solution, Rep. Math. Phys., 89(1) (2022), 81–96.
  • [3] M. Asgari, R. Ezzati, and T. Allahviranloo, Numerical solution of time-fractional order telegraph equation by Bernstein polynomials operational matrices, Math. Probl. Eng., 2016 (2016), 1–6.
  • [4] M. Amin, M. Abbas, D. Baleanu, M. K. Iqbal, and M. B. Riaz, Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation, Comput. Model. Eng. Sci., 127(1) (2021), 361–384.
  • [5] N. Alinia and M. Zarebnia, Trigonometric tension B-spline method for the solution of problems in calculus of variations, Comput. Math. and Math. Phys., 58 (2018), 631–641.
  • [6] J. Banasiak and J. R. Mika, Singularly perturbed telegraph equations with applications in the random walk theory, J. Appl. Math. Stoch. Anal., 11(1) (1998), 9–28.
  • [7] H. Bansu and S. Kumar, Numerical Solution of Space and Time Fractional Telegraph Equation: A Meshless Approach, Int. J. Nonlinear Sci. Numer. Simul., 20(3-4) (2019), 325–337.
  • [8] S. Das, K. Vishal, P. K. Gupta, and A. Yildirim, An approximate analytical solution of time-fractional telegraph equation, Appl. Math. Comput., 217(18) (2011), 7405–7411.
  • [9] H. Eltayeb, Y. T. Abdalla, I. Bachar, and M. H. Khabir, Fractional telegraph equation and its solution by natural transform decomposition method, Symmetry, 11 (2019), 334.
  • [10] W. Hachbusch, Integral equations theory and numerical treatments, Birkhäuser Basel, 1995.
  • [11] V. R. Hosseini, W. Chen, and Z. Avazzadeh, Numerical solution of fractional telegraph equation by using radial basis functions, Engineering Analysis with Boundary Elements, 38 (2014), 31–39.
  • [12] M. H. Heydari, M. R. Hooshmandasl, and F. Mohammadi, Two-dimensional Legendre wavelets for solving time-fractional telegraph equation, Adv. Appl. Math. Mech., 6(2) (2014), 247–260.
  • [13] G. Hariharan, R. Rajaraman, and M. Mahalakshmi, Wavelet method for a class of space and time fractional telegraph equations, Int. J. Phys. Sci., 7 (2012), 1591–1598.
  • [14] M. S. Hashmi, U. Aslam, J. Singh, and K. S. Nisar, An efficient numerical scheme for fractional model of telegraph equation, Alex. Eng. J., 61(8) (2022), 6383–6393.
  • [15] M. S. Hashemi and D. Baleanu, Numerical approximation of higher-order time-fractional telegraph equation by using a combination of a geometric approach and method of line, J. Comput. Phys., 316 (2016), 10–20.
  • [16] W. Ibrahim and L. K. Bijiga, Neural network method for solving time-fractional telegraph equation, Math. Probl. Eng., 2021 (2021), 1–10.
  • [17] P. Jordan and A. Puri, Digital signal propagation in dispersive media, J. Appl. Phys., 85(3) (1999), 1273–1282.
  • [18] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science BV, Amsterdam, 2006.
  • [19] K. Kumar, R. K. Pandey, and S. Yadav, Finite difference scheme for a fractional telegraph equation with generalized fractional derivative terms, Stat. A Mech. Appl., 535 (2019), 122271.
  • [20] S. Momani, Analytic and approximate solutions of the space- and time-fractional telegraph equations, Appl. Math. Comput., 176 (2005), 1126–1134.
  • [21] A. K. Mishra, S. Kumar, and A. K. Shukla, Numerical approximation of fractional telegraph equation via Legendre collocation technique, Int. J. Appl. Comput. Math., 7 (2021), 198.
  • [22] N. Mollahasani, M. M. M. Moghadam, and K. Afrooz, A new treatment based on hybrid functions to the solution of telegraph equations of fractional order, Appl. Math. Model., 40(4) (2016), 2804–2814.
  • [23] E. Orsingher and L. Beghin, Time-fractional telegraph equations and telegraph processes with Brownian time, Probab. Theory Relat. Fields, 128 (2004), 141–160.
  • [24] E. Orsingher and X. Zhao, The space-fractional telegraph equation and the related fractional telegraph process, Chin. Ann. Math. B, 24(1) (2003), 45–56.
  • [25] I. Podlubny, Fractional differential equations, Academic Press, 1999.
  • [26] P. Rahimkhani, O. Yadollah, and S. Sabermahani, Bernoulli wavelet least squares support vector regression: Robust numerical method for systems of fractional differential equations, Math. Meth. Appl. Sci., 46(17) (2023), 17641–17659.
  • [27] P. Roul, A high accuracy numerical method and its convergence for time-fractional Black-Scholes equation governing European options, Appl. Numer. Math., 151 (2020), 472–493.
  • [28] N. H. Sweilam, A. M. Nagy, and A. A. El-Sayed, Solving Time-Fractional Order Telegraph Equation Via Sinc-Legendre Collocation Method, Mediterr. J. Math., 13 (2016), 5119–5133.
  • [29] N. H. Sweilam, A. M. Nagy, and A. A. El-Sayed, Sinc-Chebyshev collocation method for time-fractional order telegraph equation, Appl. Comput. Math., 19(2) (2020), 162–174.
  • [30] F. A. Shah, M. Irfan, K. S. Nisar, and R. T. Matoog, Fibonacci wavelet method for solving time-fractional telegraph equations with Dirichlet boundary conditions, Results Phys., 24 (2021), 104123.
  • [31] S. Sabermahani, Y. Ordokhani, and S. A. Yousefi, Numerical approach based on fractional-order Lagrange poly-nomials for solving a class of fractional differential equations, Comp. Appl. Math., 37 (2018), 3846–3868.
  • [32] S. Sabermahani, Y. Ordokhani, and S. A. Yousefi, Two-dimensional Mu¨ntz–Legendre hybrid functions: theory and applications for solving fractional-order partial differential equations, Comp. Appl. Math., 39 (2020), 111.
  • [33] J. C. Strikwerda, Finite difference schemes and partial differential equations, 2nd edition, SIAM, 2004.
  • [34] O. Tasbozan and A. Esen, Quadratic B-spline Galerkin method for numerical solutions of fractional telegraph equations, Bull. Math. Sci. Appl., 18 (2017), 23–39.
  • [35] O. Tasbozan and A. Esen, Collocation solutions for the time fractional telegraph equation using cubic B-spline finite elements, An. Univ. Vest Timis. Ser. Mat.-Inf., 57(2) (2019), 131–144.
  • [36] V. A. Vyawahare and P. Nataraja, Fractional order modelling of neutron transport in a nuclear reactor, Appl. Math. Model., 37(23) (2013), 9747–9767.
  • [37] L. Wei, H. Dai, D. Zhang et al., Fully discrete local discontinuous Galerkin method for solving the fractional telegraph equation, Calcolo, 51 (2014), 175–192.
  • [38] G. Wang and M. Fang, Unified and extended form of three types of splines, J. Comput. Appl. Math., 216 (2008), 498–508.
  • [39] Y. L. Wang, M. J. Du, C. L. Temuer, and D. Tian, Using reproducing kernel for solving a class of time fractional telegraph equation with initial value conditions, Int. J. Comput. Math., 95 (2018), 1609–1621.
  • [40] X. Xu and D. Xu, Legendre wavelets direct method for the numerical solution of time-fractional order telegraph equations, Mediterr. J. Math., 15 (2018), 27.
  • [41] M. Yaseen and M. Abbas, An efficient cubic trigonometric B-spline collocation scheme for the time-fractional telegraph equation, Appl. Math. J. Chin. Univ., 35 (2020), 359–378.
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