# Numerical Starting Procedure

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:

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

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

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