Modified Semi-Analytical Approach for Duffing Equation

This research endeavour-investigates the enhanced adaptation of the Laplace-based variational iteration method (VIM) tailored specifically for tackling the Duffing Equation. This is accomplished by incorporating the Lagrange multiplier as a strategic tool to effectively address the inherent natural frequency within the Duffing Equation. Using a meticulous comparative analysis, here are juxtapose the analytical outcomes generated by the modified VIM approach with the numerical solution obtained through the application of the renowned Runge-Kutta Fehlberg method (RKF45), implemented by using the powerful mathematical software, MAPLE. Furthermore, by exploring the profound influence of diverse initial conditions on the resulting solution, a diverse array of distinct graphical representations is presented.