An efficient exponential representation for solving the two-energy group point telegraph kinetics model

•The system of the multi-energy group point telegraph model is presented.•Magnus expansion with an exponential representation of the matrix exponential function.•The relaxation times increase, the solution response is relaxed behind that of the diffusion model.•The results confirm a significant difference for PTM and PKM using various parameters.•Symmetric behavior was reported for the one-dimension homogeneous reactor of the fast and thermal neutron density.