One dimensitonal wave propogation on a string described by the wave equation u(x, t) with utt(x, t) = c2 uxx(x, t) where c = 1 is drawn as t increases. The initial conditions are u(x, 0) = I(x) and ut(x, 0) = V(x). Initial impulse V(x) occurs twice around the left end and right end of the string. Several boundary conditions are considered such as (i) fixed (ii) reflecting and (iii) open boundary conditions. For convenience the left end is assumed to be governed by (i). In other words, the left end does not move. To (iii) periodic condition can be added.
A numerical analysis is employed. For this, differential equations are discrtetized into difference equations using centered, forward or backward finite difference methods.