Document Type : Research Paper

**Authors**

Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367 Ardabil, Iran.

**Abstract**

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.

**Keywords**

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October 2021

Pages 1198-1213

**Receive Date:**31 May 2020**Revise Date:**18 November 2020**Accept Date:**06 December 2020**First Publish Date:**05 January 2021