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This paper presents a new approach and methodology to solve the second orderone dimensional hyperbolic telegraph equation with Dirichlet and Neumannboundary 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 aninterpolating function in the space dimension, with a weighted scheme. Thescheme is shown to be unconditionally stable for a range of values using thevon Neumann (Fourier) method. Several test problems are presented to confirmthe accuracy of the new scheme and to show the performance of trigonometricbasis functions. The proposed scheme is also computationally economical and canbe used to solve complex problems. The numerical results are found to be ingood agreement with known exact solutions and also with earlier studies.

Numerical Solution of second order hyperbolic telegraph equation via new Cubic Trigonometric B-Splines Approach