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Numerical solution for solving inverse telegraph equation by extended cubic B-spline | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 23، دوره 14، شماره 6، شهریور 2023، صفحه 291-302 اصل مقاله (624.13 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.22610.2391 | ||
| نویسندگان | ||
| Reza Pourgholi* ؛ Fateme Torabi | ||
| School of Mathematics and Computer Science, Damghan University, P. O. Box 36715-364, Damghan, Iran | ||
| تاریخ دریافت: 19 بهمن 1399، تاریخ پذیرش: 29 تیر 1400 | ||
| چکیده | ||
| In this paper, we consider a numerical method based on extended cubic B-spline basis functions for the determination of an unknown boundary condition in the inverse second-order one-dimensional hyperbolic telegraph equation. Extended cubic B-spline (ExCuBs) is an extension of cubic B-spline consisting of a parameter, we combined it with the Tikhonov regularization method to obtain a numerically stable solution. The convergence and stability of the technique are proved and shown that it is established under suitable assumptions and accurate order $O(k+h^2)$. The numerical results have been compared with those obtained by the cubic B-spline method to verify the accurate nature of our method. | ||
| کلیدواژهها | ||
| Extended Cubic B-spline Collocation Method؛ Stability؛ Convergence Analysis؛ Telegraph Equation | ||
| مراجع | ||
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[1] T. Akram, M. Abbas, A. I. Ismail, N.H.M. Ali and D. Baleanu, Extended cubic B-splines in the numerical solution of time fractional telegraph equation, Adv. Differ. Equ. 2019 (2019), 365. [2] W. Alharbi and S. Petrovskii, Critical domain problem for the reaction–telegraph equation model of population dynamics, Math. 6 (2018). [3] J. Banasiak and J R. Mika, Singularly perturbed telegraph equations with applications in the random walk theory, Int. J. Stochastic Anal. 11 (1998), 9–28. [4] J.G. Berryman and R. Greene Discrete inverse methods for elastic waves in layered media, Geophysics 45 (1980), 213–233. [5] N. Berwal, D. Panchal and C.L. Parihar, Haar wavelet method for numerical solution of Ttelegraph equations, Pure Appl. Math. 33 (2013), 317–328. [6] J.M.G. Cabeza, J.A.M. Garcıa and A.C. Rodrıguez,A sequential algorithm of inverse heat conduction problems using singular value decomposition, Int. J. Thermal Sci. 44 (2005), 235–244. [7] J.K. Cohen and N. Bleistein An inverse method for determining small variations in propagation speed, SIAM. J. Appl. Math. 32 (1977), 784–799. [8] C. De Boor, On the convergence of odd-degree spline interpolation, J. Approx. Theory 1 (1968), 452–463. [9] M. Dehghan and A. Ghesmati, Solution of the second-order one-dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation (DRBIE) method, Engin. Anal. Boundary Elements 34 (2010), 51–59. [10] M. Dehghan and A. Shokri, A numerical method for solving the hyperbolic telegraph equation, Numer. Meth. P.D.E. 24 (2008), 1080–1093. [11] T.M. Elzaki, E MA. Hilal and J-S.Arabia , Analytical solution for telegraph equation by modified of Sumudu transform “Elzaki transform”, Math. Theory Model. 2 (2012), 104–111. [12] A.P. Farajzadeh and J. Zafarani, Computational methods for inverse problems in geophysics: inversion of travel time observations, Physics.Earth Planet. Inter. 21 (1980), 120–125. [13] C. Hall, On error bounds for spline interpolation, J. Approx. Theory 1 (1968), 209–218. [14] A.K.A. Khalifa, Theory and applications of the collocation method with splines for ordinary and partial differential equations, Heriot-Watt University, 1979. [15] A. Kozhanov Ivanovich and R. Safiullova, Linear inverse problems for parabolic and hyperbolic equations, Dordrecht, 2010. [16] A.I. Kozhanov and R. Safiullova, Determination of parameters in telegraph equation, Ufa Math. 9 (2017), 62–74. [17] R.J. Krueger and R.L. Ochs Jr, A Green’s function approach to the determination of internal fields, Wave Motion 11 (1989), 525–543. [18] H. Latifizadeh, The sinc-collocation method for solving the telegraph equation, J. Comput. Inf. 1 (2013), 13–17. [19] J. Malinzi, A Mathematical model for oncolytic virus spread using the telegraph equation, Commun. Nonlinear Sci. Numer. Simul. 102 (2021). [20] R.C. Mittal and R. Bhatia, Numerical solution of second order one dimensional hyperbolic telegraph equation by cubic B-spline collocation method, Appl. Math. Comput. 220 (2013), 496–506. [21] R. Pourgholi and A. Saeedi Applications of cubic B-splines collocation method for solving nonlinear inverse parabolic partial differential equations, Numer. Meth. P.D.E 33 (2017), 88–104. [22] S. Sharifi and J. Rashidinia, Numerical solution of hyperbolic telegraph equation by cubic B-spline collocation method, Appl. Math. Comput. 281 (2016), 28–38. [23] H.X.L. Shengjun, An Extension of the Cubic Uniform B-Spline Curve [J], J. Comput. Aid. Design Comput. Graph. 5 (2003), 165–176. [24] S. S. Siddiqi, S. Arshed Quintic B-spline for the numerical solution of the good Boussinesq equation, J. Egypt. Math. Soc. 22 (2014), 209–213. [25] V.H. Weston and S. He, Wave splitting of the telegraph equation in R3 and its application to inverse scattering, Inv. Prob. 9 (1993). [26] H. Zeidabadi, R. Pourgholi and S. H. Tabasi, Solving a nonlinear inverse system of Burgers equations, J. Nonlinear Anal. Appl. 10 (2019), 35–54. [27] D. Zhang, F. Peng and X. Miao, A new unconditionally stable method for telegraph equation based on associated Hermite orthogonal functions, Adv. Math. Phys. 2016 (2016). | ||
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