| 44 |
certain time marks $t^{(n)}$ where $t^{(n)}=t^{(n-1)}+h$ with time step size $h>0$. In the following the upper index ${(n)}$ refers to values at time $t^{(n)}$. We use the Verlet scheme \index{Verlet scheme} with constant time step size $h$ |
certain time marks $t^{(n)}$ where $t^{(n)}=t^{(n-1)}+h$ with time step size $h>0$. In the following the upper index ${(n)}$ refers to values at time $t^{(n)}$. We use the Verlet scheme \index{Verlet scheme} with constant time step size $h$ |
| 45 |
which is defined by |
which is defined by |
| 46 |
\begin{eqnarray} \label{WAVE dyn 2} |
\begin{eqnarray} \label{WAVE dyn 2} |
| 47 |
u^{(n)}=2u^{(n-1)}-u^{(n)} + h^2 a^{(n)} \\ |
u^{(n)}=2u^{(n-1)}-u^{(n-2)} + h^2 a^{(n)} \\ |
| 48 |
\end{eqnarray} |
\end{eqnarray} |
| 49 |
for all $n=1,2,\ldots$. It is designed to solve a system of equations of the form |
for all $n=1,2,\ldots$. It is designed to solve a system of equations of the form |
| 50 |
\begin{eqnarray} \label{WAVE dyn 2b} |
\begin{eqnarray} \label{WAVE dyn 2b} |
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