An artificial parameter Linstedt–Poincaré method for the periodic solutions of nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable

An artificial parameter Linstedt–Poincaré method is presented and used to determine the periodic solution of a nonlinear singular oscillator for small and large amplitudes. Comparisons with the results of harmonic balance, two-level iterative, linearized harmonic balance and parameter perturbation methods are presented.