  This paper deals with a construction of new algorithm: the modified
trigonometric cubic B-Spline differential quadrature (MTB-DQM) for space
discretization together with a time integration algorithm" for numerical
computation of the hyperbolic equations. Specially, MTB-DQM has been
implemented for the initial value system of the telegraph equations together
with both Dirichlet and Neumann type boundary conditions. The MTB-DQM is a DQM
based on modified trigonometric cubic B-splines as new base functions. The
problem has been reduced into an amenable system of ordinary differential
equations adopting MTB-DQM. The resulting system of ordinary differential
equations is solved using time integration algorithms. Further, the stability
of MTB-DQM is studied by computing the eigenvalues of the coefficients matrices
for various grid points, which confirmed the stability of MTB-DQM for the
telegraphic equations. The accuracy of the method has been illustrated in terms
of the various discrete error norms for six test problems of the telegraph
equation. A comparison of computed numerical solutions with that obtained by
the other methods has been carried out for various time levels considering
various space sizes
