Analytical approximate solution of fourth-order weakly non-linear differential systems based on unified KBM method with strong damping and slowly varying co-efficients

摘要

An approximate analytic technique is presented for obtaining the solution of fourth-order weakly non-linear differential systems with strong damping and slowly varying co-efficients based on unified Krylov-Bogoliubov-Mitropolskii (KBM) method. The first-order approximate solutions for different initial conditions show good agreement with those of numerical solutions obtained by the fourth-order Runge-Kutta method and these are compared graphically. Also some limitations of the KBM method are discussed. An example is given for justifying the method.