پیوندهای مفید
آمار
| تعداد نشریات | 22 |
| تعداد شمارهها | 708 |
| تعداد مقالات | 10,204 |
| تعداد مشاهده مقاله | 71,617,072 |
| تعداد دریافت فایل اصل مقاله | 63,421,372 |
A new approach for solution of telegraph equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 29، دوره 12، شماره 1، مرداد 2021، صفحه 385-396 اصل مقاله (1.26 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4811 | ||
| نویسندگان | ||
| Mohammad Zarebnia* 1؛ Reza Parvaz2 | ||
| 1Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367 Ardabil, Iran | ||
| 2Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367 Ardabil, Iran | ||
| تاریخ دریافت: 07 شهریور 1396، تاریخ بازنگری: 13 آبان 1398، تاریخ پذیرش: 31 تیر 1399 | ||
| چکیده | ||
| In this paper, B-spline collocation method is developed for the solution of one-dimensional hyperbolic telegraph equation. The convergence of the method is proved. Also the method is applied on some test examples and the numerical results have been compared with the analytical solutions. The $L_\infty$,$L_2$ and Root-Mean-Square errors (RMS) in the solutions show the efficiency of the method computationally. | ||
| کلیدواژهها | ||
| Telegraph equation؛ Collocation method؛ Convergence | ||
| مراجع | ||
|
[1] A. Atangana, On the stability and convergence of the time-fractional variable order telegraph equation, J. Comput. Phys. 293 (2015) 104–114. [2] R.C. Cascaval, E. Eckstein, C.L. Frota, J.A. Goldstein, Fractional telegraph equations, J. Math. Ana. Appl. 276(1) (2002) 145–159. [3] V. Devi, R.K. Maurya, S. Singh, V.K. Singh, Lagranges operational approach for the approximate solution of two-dimensional hyperbolic telegraph equation subject to Dirichlet boundary conditions, Appl. Math. Comput. 367 (2020) 124717. [4] H.F. Ding, Y.X. Zhangb, J.X Caoa and J.H Tianb, A class of difference scheme for solving telegraph equation by new non-polynomial spline methods, Appl. Math. Comput. 278 (2012) 4671–4683. [5] F. Gao and C. Chi, Unconditionally stable difference schemes for a one-space-dimensional linear hyperbolic equation, Appl. Math. Comput. 187 (2007) 1272–1276. [6] R. Jiwari, S. Pandit and R.C. Mittal, A differential quadrature algorithm for solution of the second order one-dimensional hyperbolic telegraph equation, IJNS 13 (2012) 259–266. [7] S.A. Khuri and A. Sayfy, A spline collocation approach for the numerical solution of a generalized nonlinear Klein Gordon equation, Appl. Math. Comput. 216 (2010) 1047–1056. [8] A.C. Metaxas and R.J. Meredith, Industrial Microwave, Heating, Peter Peregrinus, London, 1993. [9] R.C. Mittal and R. Bhatia, A numerical study of two-dimensional hyperbolic telegraph equation by modified B-spline differential quadrature method, Appl. Math. Comput. 244 (2014) 976–997. [10] R.K. Mohanty, M.K. Jain and K. George, On the use of high order difference methods for the system of one space second order nonlinear hyperbolic equations with variable coefficients, J. Comput. Appl. Math. 72 (1996)421–431. [11] R.K. Mohanty, An unconditionally stable finite difference formula for a linear second order one space dimensional hyperbolic equation with variable coefficients, Appl. Math. Comput. 165 (2005) 229–236. [12] G. Pittaluga and L. Sacripante, Quantic spline interpolation on uniform meshes, Acta. Math. Hung. 72 (1996) 4167–175. [13] P.M. Prenter, Spline and Variational Methods, Wiley, New York, 1975. [14] G. Roussy and J. A. Pearcy, Foundations and Industrial Applications of Microwaves and Radio Frequency Fields, John Wiley, New York, 1995. [15] P. Sancho, Relativistic Extension of the Quantum Telegraph Equation, Open. Syst. Inf. Dyn. 7(2) (2000) 157–164. [16] J. N. Sharma, K. Singh and J. N. Sharma, Partial Differential Equations for Engineers and Scientists, second edition, Alpha Science International, 2009. [17] J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, third edition, Springer-Verlg, 2002. [18] M. Zarebnia and R. Parvaz, Cubic B-spline collocation method for numerical solution of the one-dimensional hyperbolic telegraph equation, JARSC 4(4) (2012) 46–60. | ||
|
آمار تعداد مشاهده مقاله: 15,981 تعداد دریافت فایل اصل مقاله: 10,005 |
||