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Zarebnia, Mohammad, Parvaz, Reza. (1400). An approximation to the solution of one-dimensional hyperbolic telegraph equation based on the collocation of quadratic B-spline functions. سامانه مدیریت نشریات علمی, 9(4), 1198-1213. doi: 10.22034/cmde.2020.40112.1749
Mohammad Zarebnia; Reza Parvaz. "An approximation to the solution of one-dimensional hyperbolic telegraph equation based on the collocation of quadratic B-spline functions". سامانه مدیریت نشریات علمی, 9, 4, 1400, 1198-1213. doi: 10.22034/cmde.2020.40112.1749
Zarebnia, Mohammad, Parvaz, Reza. (1400). 'An approximation to the solution of one-dimensional hyperbolic telegraph equation based on the collocation of quadratic B-spline functions', سامانه مدیریت نشریات علمی, 9(4), pp. 1198-1213. doi: 10.22034/cmde.2020.40112.1749
Zarebnia, Mohammad, Parvaz, Reza. An approximation to the solution of one-dimensional hyperbolic telegraph equation based on the collocation of quadratic B-spline functions. سامانه مدیریت نشریات علمی, 1400; 9(4): 1198-1213. doi: 10.22034/cmde.2020.40112.1749

An approximation to the solution of one-dimensional hyperbolic telegraph equation based on the collocation of quadratic B-spline functions

Computational Methods for Differential Equations
مقاله 18، دوره 9، شماره 4، دی 2021، صفحه 1198-1213  XML اصل مقاله (4.5 MB)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.40112.1749
نویسندگان
Mohammad Zarebnia email ؛ Reza Parvaz
Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367 Ardabil, Iran.
چکیده
In this work, the collocation method based on B-spline functions is used to obtain a numerical solution for a one-dimensional hyperbolic telegraph equation. The proposed method is consists of two main steps. As the first step, by using a finite difference scheme for the time variable, a partial differential equation is converted to an ordinary differential equation by the space variable. In the next step, for solving this equation collocation method is used. In the analysis section of the proposed method, the convergence of the method is studied. Also, some numerical results are given to demonstrate the validity and applicability of the presented technique. The L∞, L2, and Root-Mean Square(RMS) in the solutions show the efficiency of the method computationally.
کلیدواژه‌ها
Quadratic B-spline؛ One-dimensional hyperbolic telegraph equation؛ Collocation method؛ Convergence analysis
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