  This paper presents a new approach and methodology to solve the second order
one dimensional hyperbolic telegraph equation with Dirichlet and Neumann
boundary conditions using the cubic trigonometric B-spline collocation method.
The usual finite difference scheme is used to discretize the time derivative.
The cubic trigonometric B-spline basis functions are utilized as an
interpolating function in the space dimension, with a weighted scheme. The
scheme is shown to be unconditionally stable for a range of values using the
von Neumann (Fourier) method. Several test problems are presented to confirm
the accuracy of the new scheme and to show the performance of trigonometric
basis functions. The proposed scheme is also computationally economical and can
be used to solve complex problems. The numerical results are found to be in
good agreement with known exact solutions and also with earlier studies.
