PERIODIC SOLUTIONS FOR CERTAIN NON-SMOOTH OSCILLATORS WITH HIGH NONLINEARITIES

In this paper, we introduce a new adjustment of the Lindstedt-Poincare method combining it homotopy in topology by introducing a linear term with an unknown (variable) frequency and amplitude to be determined further and the solutions are in form of series expansions and maybe converge asymptotically. This adjustment works very well for nonsmooth oscillators with high nonlinearities. Examples given confirm that only one or two iterations lead to high accuracy of the solutions.