A modification of the stiefel-bettis method for nonlinearly damped oscillators

We report a modification of the Stiefel-Bettis method which is of trigonometric order one and of polynomial order two for the general second order initial value problems. We also discuss the modified Stiefel-Bettis method made explicit for the undamped nonlinear oscillators. Numerical solution of problems are given to illustrate the methods.