Methods to Increase Efficiency

Computer simulations of a classical many-particle system are based on the solution of the Newtonian equations  $$m_{k}\frac{d^{2}}{dt^{2}}\vec{r}_{k}=\vec{F}_{k}(\vec{r}_{1},\ldots ,\vec{r}_{{\mbox{$\scriptstyle\cal N$ }}})\quad ,$$
where $\vec{r}_{k}$ denotes the position and m_k the mass of particle k, $k=1,2,\ldots,\mbox{$\cal N$ }$, $\cal N$