KB method for obtaining an approximate solution of slowly varing amplitude and phase of nonlinear differential systems with varying coefficients

Abstract

To determine an approximate solutions of damped nonlinear ordinary differential system with varying coefficients of oscillatory procedure is envisaged based on the Krylov-Bogoliubov (KB) method. Our aim is to this paper of Krylov and Bogoliubov (KB) for determining an approximate solution of a nonlinear differential system with varying coefficients. Finally, results are discussed, especially to enrich the physical prospects, and shown graphically by utilizing Mathematica and Mathlab software. However, in some cases it’s feasible to alternate nonlinear differential equations with an associated linear equation closely enough to give helpful results. Some expository examples are given to exhibit the suitability and proficiency considered method.