The explicit central difference method and the implicit Newmark method was combined with the Chebyshev spectral element method

respectively

and their influences on the numerical error and stability were studied. The process of one noise disturbance spreading in freedom space was simulated and the numerical errors of the two time-difference methods were compared with each other and the stability of the central difference method was investigated. The conclusions can be drawn that both the two time-difference methods can acquire right numerical result. The explicit central difference method has higher accuracy than the implicit one and the numerical error of the Newmark method is about twice that of the explicit central difference method when the central difference method is stable. Moreover

the result of central difference method is divergent when the time step used is larger than the critical step while the numerical result of the Newmark method still is coincident with the reference solution obtained by the analytical method.