Numerical solutions to wave equation Does the wave equation always have an analytical solution given well-behaved boundary/initial conditions? If not, under what conditions does the wave equation need to be solved numerically?  This figure of a simple 1D-problem seems to have been generated numerically.
Any recommended reading for general theory on the wave equation is also welcome.

Stein & Shakarchi introduction to Fourier analysis is also a good reference, where the theory of wave equations is well developed, a main tool to find solutions is the Fourier transfom.
