A modified method of averaging for solving a class of nonlinear equations

In this paper, we studied a method of averaging which decide a uniform validsolution for nonlinear equationand got the ,modified forms for KB ,method (Krylov-Bogoliubov method)and KBMmethod (Krytov-Bogoliubov-Mitropolski method). Through the comparison of two examples with the method of multiple scales it can be shown that the modifies averaging methods here are uniformly valid and thereby the applied area of the methodof averaging are extended.