This paper has proposed a local differential transform method in analysing various types of linear and nonlinear initial value problems (IVP) representing physical models encountered in a broad range of science. Local and global error analyses of the proposed scheme are presented to demonstrate the capacity and priorities of the local differential transform method (LDTM). The produced results show that even using coarser meshes the present scheme produce quite a little error in finite time. The present solution technique in solving the IVPs is compared with the Runge-Kutta method. It is proved that the LDTM produces more accurate results than the Runge-Kutta methods studied in the literature. By considering various types of initial value problems, the stabilities of the LDTM and the RK4 are examined with various time intervals in a comparative way.