 # Diff of /trunk/doc/user/wave.tex

revision 574 by gross, Mon Feb 27 00:04:17 2006 UTC revision 575 by lkettle, Fri Mar 3 03:33:07 2006 UTC
# Line 44  We use an explicit time-integration sche Line 44  We use an explicit time-integration sche
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}

Legend:
 Removed from v.574 changed lines Added in v.575