A numerical method for the nonlinear oscillator problem

The treatment of a nonlinear Schrِdinger equation with power law potential terms by means of hypervirial perturbation theory (HVPT) is considered. Previous workers have tried to handle the nonlinearity by constructing an HVPT which also contains a nonlinear term. We show that higher numerical accuracy can be obtained by reverting to the usual linear HVPT in combination with a simple numerical procedure. The procedure also works with finite-difference shooting calculations, which would permit the calculations to be extended to handle more general potentials.