This problem was developed from a description found in Fox et al. (1988) Solving
Problems on Concurrent Processors, vol. 1. Prentice Hall.
Calculate the amplitude along a uniform, vibrating string after a specified amount
of time has elapsed.
Numerical Solution
First, impose a framework on the problem.
The framework consists of amplitude A on the y axis and index i on the
x axis, where i represents the position in the regular grid of points imposed along the
length of the string. The amplitude is to be updated at discrete time steps.
The equation to be solved is the finite-difference approximation to the one-dimensional
wave equation:
A(i,t+1) = 2.0*A(i,t) - A(i,t-1)
+ c * (A(i-1,t) - 2.0*A(i,t) + A(i+1,t))
where c is a constant.
Note that the amplitude at (i, t+1) depends on two previous timesteps (t and t-1) as
well as two neighboring points (i-1 and i+1). Thus, both initial and boundary data are
required in order to loop to the new timestep (t+1).
