The computing times for the PIM, RK, and MFPC to calculate the responses of the system in 100 seconds are shown in Table 1.
Choosing the number of Laguerre points as n = 30, the time history curves of displacements [x.sub.1] obtained by MFPC, PIM, and LK with different time steps are shown in Figure 8.
Table 2 shows the comparison of the computing times of the MFPC, PIM, and RK upon calculating the responses of system (2) over [0,100].
Compared with the Runge-Kutta method and MFPC, the PIM is able to obtain very accurate solutions much more efficiently.
Caption: Figure 4: Absolute errors of the displacements x([tau]) obtained by PIM, RK, and MFPC.
Caption: Figure 6: Comparison of the amplitudes versus the external force f obtained by the MFPC and PIM.
Caption: Figure 7: Comparison of the amplitude-frequency curve versus the external force [omega] obtained by the MFPC and PIM.
Caption: Figure 9: Absolute errors of the displacements [x.sub.1]([tau]) for system (21) obtained by PIM, RK, and MFPC, respectively.