# What are the good testing problems for hyperbolic equation?

I read the whole list of this question: Where can one obtain good data sets/test problems for testing algorithms/routines? But the answers are in different areas and I want to ask a specific area.

I am looking for resting problems for wave equation, telegraph equation or Klein-Gordon equation, etc. What they have in common is that they are second-order linear hyperbolic partial differential equations. By testing problem, I mean those can show how well my numerical algorithms behaved, which is exactly the meaning in the similar question I listed above.

• You can use the method of manufactured solutions to come up with test problems for any equation. – Aurelius Oct 30 '14 at 22:57
• How many spatial dimensions are you interested in? – David Ketcheson Nov 2 '14 at 7:27
• Since these equations can be solved (in simple geometries) exactly by classical Fourier analysis, it seems trivial to come up with test problems. – David Ketcheson Nov 2 '14 at 7:29