Formulae of centered-difference approximations of first- and second-order partial derivatives of the function u(x, t) in spatial domain based on Taylor series expansions are presented in many literatures of Finite Difference Method (FDM). This approach is also understood as a very basic algorithm. In this paper, we investigate the other approach which is to use higher-order Finite Element (HO-FE) analysis to formulate the 2Mth-order centered-difference approximations of M=1÷9. The obtained results have been seen that formulae of higher-order central FE and FD approximations are similar and the proposed approach is simpler than the one of Taylor series expansions. From this investigation, general formulae of 2Mth-order FD approximations of any M≥1 are expressed. In addition, an introduction to a kind of Meshless Methods, Smooth Particle Hydrodynamics (SPH) method, is also presented. Finally, three numerical methods are applied to calculate lightning-induced voltages on multiconductor distribution lines by solving Field-to-transmission line coupling equations. The solutions of various numerical methods are illustrated and compared by means of graphs.
