New solutions of hyperbolic telegraph equation

We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP is applied in numerically discretized ordinary differential equations obtained from application FTI to given partial equation (PDE). algorithm hyperbolic telegraph utilizes the Cayley transformation Pade approximations Minkowski space. It avoids unauthentic solutions ghost fixed points which one advantages over other related numerical methods literature. technique tested three specific examples for various parameter values appearing discretization steps. Such are first this paper. Illustrative figures provided. Efficiency determined by an error analysis achieved comparing with exact solutions.