Krylov-Bogoliubov-Mitropolskii method for fifth order critically damped nonlinear systems in the case for large equal eigenvalues

Abstract

In this article, we have considered a fifth order critically damped nonlinear differential system, and studied the asymptotic solutions when two of the eigenvalues are large and equal and the other eigenvalues are distinct. In this study, we have found that the approximate results obtained by the modified KBM method corresponds with those obtained by the numerical method using Mathematica.