Finding the solution to the wave equation on a closed interval (non-zero boundaries)
Hey guys, apologies if this is in the wrong section. I know wave equations are a type of differential equation, but for this particular question I'm not really solving the DE as such. My course is called Applied Analysis so I thought this would be the place to put the question.
We were given the following wave equation with initial- and boundary-conditions:
We were then asked to compute u(3/2, 3/2) using an "appropriate characteristic parallelogram". I know that the characteristics are x-t = 0 and x+t = 0 and that the solution to this problem is u(3/2, 3/2) = u(A) + u(B) - u(C), but finding the points for my parallelogram is proving to me quite confusing as my geometry is seriously shocking. I know that this is a simple question with a simple solution.
The solution has the points (1,1), (2,1) and (3/2, 1/2) all in region III, so if I could get some help as to how these points were found, that would be great.