Wave 2D

Solves the two-dimensional wave equation using the position Verlet algorithm.

\[ \frac{\partial^2 U}{\partial t^2} - c^2\frac{\partial^2 U}{\partial x^2} = 0 \]

where \(U=u(x,y,t)\) defined on the domains \(x\in[0,1], y\in[0,1]\) and \(t\in[0,1]\), and wave speed \(c=1\). The boundaries are Dirichlet. Initial position and velocity are given as

\[ u(x,y,0) = \sin(\pi x) \sin(\pi y) \]

\[ u'(x,y,0) = 0 \]