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

N coupled non-local harmonic oscillators leading to 2N-th order initial value problem