Numerical solution for solving inverse telegraph equation by extended cubic B-spline

Document Type : Research Paper


School of Mathematics and Computer Science, Damghan University, P. O. Box 36715-364, Damghan, Iran


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 $O(k+h^2)$. The numerical results have been compared with those obtained by the cubic B-spline method to verify the accurate nature of our method.


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Volume 14, Issue 6
June 2023
Pages 291-302
  • Receive Date: 07 February 2021
  • Accept Date: 20 July 2021
  • First Publish Date: 09 October 2022