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

Abstract

In this work, collocation method based on B-spline functions is used to obtained a numerical solution for one-dimensional hyperbolic telegraph equation. The proposed method is consists of two main steps. As first step, by using finite difference scheme for time variable, partial differential equation is converted to an ordinary differential equation by 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.