Numerical solution of hyperbolic telegraph equation by cubic B-spline collocation method

We present a collocation method based on redefined extended cubic B-spline basis functions to solve the second-order one-dimensional hyperbolic telegraph equation. Extended cubic B-spline is an extension of cubic B-spline consisting of a parameter. The convergence and Stability of the method are proved and shown that it is unconditionally stable and accurate of order O(k+h2)O(k+h2). Computational efficiency of the method is confirmed through numerical examples whose results are in good agreement with theory. The obtained numerical results have been compared with the results obtained by some existing methods to verify the accurate nature of our method. The advantage of this approach is that it can be conveniently used to solve problem and it is also capable of reducing the size of computational work.