A numerical approximation for the solution of a time-fractional telegraph equation by the moving least squares approach

Hajinezhad, Haniye; Soheili, Ali R.

doi:10.22034/cmde.2023.55070.2286

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	A numerical approximation for the solution of a time-fractional telegraph equation by the moving least squares approach
Computational Methods for Differential Equations
مقاله 4، دوره 11، شماره 4، مهر 2023، صفحه 716-726 اصل مقاله (719.4 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.55070.2286
نویسندگان
Haniye Hajinezhad^* ¹؛ Ali R. Soheili²
¹Department of Mathematics, Payame Noor University, Tehran, Iran.
²Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.
چکیده
This paper focuses on the numerical solution of the time-fractional telegraph equation in Caputo sense with $1 < \beta < 2$. The time-fractional telegraph equation models neutron transport inside the core of a nuclear reactor. The proposed numerical solution consists of two stages. First, the time-discretized scheme of this equation is obtained by the Crank-Nicolson method. The stability and convergence of results from the semi-discretized scheme are presented. In the second stage, the numerical approximation of the unknown function at specific points is achieved through the collocation method using the moving least square method. The numerical experiments analyze the impact of some parameters of the proposed method.
کلیدواژه‌ها
Time-Fractional telegraph equation؛ Moving least squares method؛ Stability؛ Convergence

مراجع
[1] A. Babu, et al., Numerical solution of the hyperbolic telegraph equation using cubic B-spline-based differential quadrature of high accuracy, Computational Methods for Differential Equations, 10(4) (2022), 837–859. [2] J. Banasiak and J. R. Mika, Singularly perturbed telegraph equations with applications in the random walk theory, Journal of Applied Mathematics and Stochastic Analysis, 11(1) (1998), 9–28. [3] T. Belytschko, et al., Smoothing and accelerated computations in the element free Galerkin method, Journal of computational and applied mathematics, 74(1-2) (1996), 111–126. [4] H. Hajinezhad and A. R. Soheili, A numerical approximation for the solution of a time–fractional telegraph equation based on the Crank–Nicolson method, Iranian journal of numerical analysis and optimization, 12(3) (Special Issue) (2022), 607–628. [5] V. R. Hosseini, et al., Numerical solution of fractional telegraph equation by using radial basis functions, Engi- neering Analysis with Boundary Elements, 38 (2014), 31–39. [6] M. Javidi, et al., (2021). Numerical solution of fractional Riesz space telegraph equation, Computational Methods for Differential Equations, 9(1) (2021), 187–210. [7] A. Kumar, et al., A local meshless method to approximate the time-fractional telegraph equation, Engineering with Computers, 37(4) (2021), 3473–3488. [8] P. Lancaster and K. Salkauskas, Surfaces generated by moving least squares methods, Mathematics of computation, 37(155) (1981), 141–158. [9] C. Li and A. Chen, Numerical methods for fractional partial differential equations, International Journal of Com- puter Mathematics, 95(6-7) (2018), 1048-1099. [10] G. R. Liu and Y. T. Gu, An introduction to meshfree methods and their programming, Springer Science and Business Media, (2005). [11] G. R. Liu and M. B. Liu, Smoothed particle hydrodynamics– a meshfree particle method, World Scientific, Singa- pore, (2003). [12] A. Mohebbi, et al., The meshless method of radial basis functions for the numerical solution of time fractional telegraph equation, International Journal of Numerical Methods for Heat and Fluid Flow, 24(8) (2014), 1636–1659. [13] S. Niknam and H. Adibi, A numerical solution of two-dimensional hyperbolic telegraph equation based on moving least square meshless method and radial basis functions, Computational Methods for Differential Equations, 10(4) (2022), 969–985. [14] O. Nikan, et al., Numerical approximation of the nonlinear time-fractional telegraph equation arising in neutron transport, Communications in Nonlinear Science and Numerical Simulation, 99 (2021). [15] Z. M. Odibat and S. Momani, An algorithm for the numerical solution of differential equations of fractional order, Journal of Applied Mathematics and Informatics 26(1-2) (2008), 15–27. [16] B. Sepehrian and Z. Shamohammadi, Numerical solution of nonlinear time-fractional telegraph equation by radial basis function collocation method, Iranian Journal of Science and Technology, Transactions A: Science, 42(4) (2018), 2091–2104. [17] K. Shah, et al., Stable numerical results to a class of time-space fractional partial differential equations via spectral method, Journal of Advanced Research, 2 (2020), 39–48. [18] K. Shah, et al., Evaluation of one dimensional fuzzy fractional partial differential equations, Alexandria Engineer- ing Journal, 59(5) (2020), 3347–3353. [19] E. Shivanian, Spectral meshless radial point interpolation (SMRPI) method to two-dimensional fractional telegraph equation, Mathematical Methods in the Applied Sciences, 39(7) (2016), 1820–1835. [20] E. Shivanian, et al., Local integration of 2-D fractional telegraph equation via moving least squares approximation, Engineering Analysis with Boundary Elements, 56 (2015), 98–105. [21] N. H. Sweilam, et al., (2020). Sinc-Chebyshev collocation method for time-fractional order telegraph equation, Appl. Comput. Math, 19(2) (2020), 162–174. [22] V. A. Vyawahare and P. Nataraj, Fractional-order modeling of neutron transport in a nuclear reactor, Applied Mathematical Modelling, 37(23) (2013), 9747–9767.
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A numerical approximation for the solution of a time-fractional telegraph equation by the moving least squares approach