Numerical mountain pass periodic solutions of a nonlinear spring equation

In this paper, we show how the introduction of a nonlinear term in the classic spring model can produce dramatic results. We compute a large amplitude solution which is drastically different from the known linear, small amplitude solution. A dual variational formulation is given, recasting the problem as one in which saddle points correspond to solutions of the differential equation. Our computations are based on the numerical mountain pass algorithm developed by Choi and McKenna which was inspired by the theorems of Ambrosetti, Rabinowitz and Ekeland.