A piecewise analytical iterative method for a wire-mass model

Abstract

A wire-mass model is considered, where the wire is elastic and the mass is attached to the wire. We propose a piecewise analytical iterative method for simulating the motion of the mass attached to the wire. Our proposed method combines Picard’s successive approximation and Taylor series expansion methods. Picard’s successive approximation method is simple to construct, but difficult to compute, as it involves a nonlinear term in the integrand. Taylor series expansion method is accurate, but only for small intervals. We combine these two methods to take advantage of the strengths and avoid the weaknesses of both methods. Therefore, we implement this combination piecewisely. Numerical tests show that our proposed method is simple to implement but produces accurate solutions.