Next: Damage of a homogeneous Up: Dynamics of damage in Previous: Dynamics Contents

Numerical Algorithm

Rewrite as

$\begin{displaymath} \dot{\bf z_i} = {\bf p_i}, \ \dot{\bf p_i} = \frac{1}{m_... ...rt z_i -z_j\vert)}{{\bf \vert z_i -z_j\vert}}({\bf z_i -z_j}). \end{displaymath}$

(5)

Introducing the notation

$\begin{displaymath}\vec{\bf x} = \left\{ {\bf z_i}, {\bf p_i} \right\}, \ \... ... p_i}, \frac{1}{m_i} (\phi_i - \gamma {\bf p_i}) \right\} , \end{displaymath}$

we get

$\begin{displaymath}\dot{\vec{\bf x}} = \vec{\bf f}(\vec{\bf x}).\end{displaymath}$

$\begin{displaymath} {\vec{\bf x}}_{n+1} = {\vec{\bf x}}_n + \frac{k}{2} \left... ...f f}(\vec{\bf x}_n + h \vec{\bf f}(\vec{\bf x}_n)) \right). \end{displaymath}$

(6)

Liya Zhornitskaya 2002-06-19