At time
$t=0$
, the displacement $u$
and velocity
${\dot{u}}_{0}$
are known from initial conditions. The acceleration
${\ddot{u}}_{0}$
and time step
${h}_{1}$
are found from solving the equations of motion. The initial
time step
${h}_{0}$
is set to zero:(1)
(2)
(3)

$${h}_{0}=0\text{\hspace{1em}};\text{\hspace{1em}}{h}_{\frac{1}{2}}=\frac{{h}_{1}}{2}$$

$${\dot{u}}_{-\frac{1}{2}}={\dot{u}}_{0}$$

$${\dot{u}}_{\frac{1}{2}}={\dot{u}}_{0}+{h}_{\frac{1}{2}}{\ddot{u}}_{0}$$