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.

Derivation
Solutions
It has a general solution but numerical solutions can still be an interesting exercise. Numerical solutions are useful when you are solving some variation of the wave equation with an additional term in it which makes it unsolvable analytically. 
