  We consider a set of interwoven harmonic oscillators where the acceleration
of a given oscillator is determined by the position of its nearest neighbor. We
show that this problem of N non-local oscillators with periodic boundary
conditions leads to a 2N-th order initial value problem. We discuss the
numerical solution of this using a non-polynomial spline method. A very precise
numerical method that minimizes the error can be developed, which we test for a
few examples of driving forces.
