University of Tabriz Computational Methods for Differential Equations 2345-3982 9 4 2021 10 01 An approximation to the solution of one-dimensional hyperbolic telegraph equation based on the collocation of quadratic B-spline functions 1198 1213 12204 10.22034/cmde.2020.40112.1749 EN Mohammad Zarebnia Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367 Ardabil, Iran. Reza Parvaz Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367 Ardabil, Iran. Journal Article 2020 05 31 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. https://cmde.tabrizu.ac.ir/article_12204_b1c4be24321a38047cbae03e43e63e66.pdf