numerical solution for solving inverse telegraph equation by extended cubic b-spline

In this paper, we consider a numerical method based on extended cubic b-spline basis functions for the determination of an unknown boundary condition in the inverse second-order one-dimensional hyperbolic telegraph equation. extended cubic b-spline (excubs) is an extension of cubic b-spline consisting of a parameter, we combined it with the tikhonov regularization method to obtain a numerically stable solution. the convergence and stability of the technique are proved and shown that it is established under suitable assumptions and accurate order o(k + h2). the numerical results have been compared with those obtained by the cubic b-spline method to verify the accurate nature of our method.