Leung, Andrew Yee TakAndrew Yee TakLeungZhang, Q. C.2022-03-302022-03-302003https://repository.sfu.edu.hk/handle/sfu/2819An efficient method for calculating the normal form and the associated non-linear transformations for the semi-simple case without central manifold reduction is given in this paper. The one-step transformation concept is adopted for easy programming. This method can be used to calculate high order normal forms of high-dimensional ordinary differential equations of non-linear oscillators. A program in MATHEMATICA language is designed to perform the calculation. Three examples are given in order to verify the method and to show the efficiency of the program.enjournal article10.1016/S0022-460X(02)01626-7