Wave 1D Case 2#
Solves the one-way wave equation using the position Verlet or Forest-Ruth algorithms with higher wave speed.
\[
\frac{\partial^2 U}{\partial t^2} - c^2\frac{\partial^2 U}{\partial x^2} = 0
\]
where \(U=u(x,t)\) defined on the domains \(x\in[0,1]\) and \(t\in[0,0.06]\), and wave speed \(c=100\). Initial position and velocity are given as
\[\begin{split}
u(x,0) = \begin{cases}
\sin(\pi x) & 2 < x < 3 \\
0 & \text{ otherwise }
\end{cases}
\end{split}\]
\[
u'(x,0) = 0
\]