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We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP method is applied in numerically discretized ordinary differential equations obtained from application of FTI method to a given partial differential equation ( PDE). The algorithm is applied to hyperbolic telegraph equation and utilizes the Cayley transformation and the Pade approximations in the Minkowski space. It avoids unauthentic solutions and ghost fixed points whichdoi:10.3934/jdg.2020029 fatcat:4m755kvsjvbs5ez75m4vy7u26q