# Which explicit method is used in the RF-DYNAM Pro - Nonlinear Time History add-on module?

The RF-DYNAM Pro - Nonlinear Time History offers, in addition to the implicit NEWMARK method of mean acceleration, also an explicit method.

It should be noted that not the "original" version of the central difference method is used here, but a modified form. The modified form is characterized by the fact that it is simply not a central difference when applying the speed difference. The following two equations show the applied differences of velocity and acceleration:

Speed: (no central difference)

${\dot{\mathrm x}}_{\mathrm n+1/2}=\frac{{\mathrm x}_{\mathrm n+1}-{\mathrm x}_\mathrm n}{{\mathrm{Δt}}_{\mathrm n+0,5}}$

Acceleration: (central difference)

${\ddot{\mathrm x}}_\mathrm n=\frac{{\dot{\mathrm x}}_{\mathrm n+0,5}-{\dot{\mathrm x}}_{\mathrm n-0,5}}{{\mathrm{Δt}}_\mathrm n}$

This approach leads to a faster convergence since it responds "faster" to changes in loading or structure (nonlinearities). When to select the explicit analysis is described in detail in FAQ 2356 .

#### Reference

 [1] Manual RF-DYNAM Pro. (2020). Tiefenbach: Dlubal Software.