We propose a simple and accurate numerical scheme for solving the time fractional
telegraph (TFT) equation within Caputo type fractional derivative. A fictitious
coordinate ϑ is imposed into the problem in order to transform the dependent
variable u(x, t) into a new variable with an extra dimension. In the new space with
the added fictitious dimension, a combination of method of line and group preserving
scheme (GPS) is proposed to find the approximate solutions. This method preserves
the geometric structure of the problem. Power and accuracy of this method has been
illustrated through some examples of TFT equation.