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Numerical solution of fractional Riesz space telegraph equation | ||
| Computational Methods for Differential Equations | ||
| مقاله 12، دوره 9، شماره 1، فروردین 2021، صفحه 187-210 اصل مقاله (1.69 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2019.33771.1551 | ||
| نویسندگان | ||
| Mohammad Javidi* 1؛ Malek Ahmadian Asl2؛ Farhad Dastmalci Saei2؛ Yaghoub Mahmoudi2 | ||
| 1Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran. | ||
| 2Departement of Mathematics, Islamic Azad University Tabriz Branch, Tabriz, Iran. | ||
| چکیده | ||
| In this paper, a numerical method based on polynomial approximation is presented for the Riesz fractional telegraph equation. First, a system of fractional differential equations are obtained from the telegraph equation with respect to the time variable by using the method of lines. Then a new numerical algorithm, as well as its modification for solving fractional differential equations (FDEs) based on the polynomial interpolation, is proposed. The algorithms are designed to estimate to linear fractional systems. The convergence order and stability of the fractional order algorithms are proved. At the end three examples with known exact solutions are chosen. Numerical results show that accuracy of present scheme is of order O(∆t 2 ). | ||
| کلیدواژهها | ||
| Fractional telegraph equation؛ Polynomial approximation؛ Riemann-Liouville fractional derivative؛ Riesz fractional equation؛ Discretization | ||
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