Multistage Optimal Parametric Iteration Method Applied to Generate Closed-Form Solutions for Dynamical System with Quadratic Nonlinearities

This paper investigates the damped and periodical oscillations of a specific system that depends on four physical parameters. Exact parametric solutions are established based on a smooth function. The system is explicitly integrated without admitting prime integrals. The influence of the physical parameters is examined semi-analytically through the Multistage Optimal Parametric Iteration Method (MOPIM). A key advantage of this method is that it used only one iteration, owing to an appropriate choice of auxiliary functions for convergence control. There is accuracy between MOPIM solutions and corresponding numerical results, highlighted qualitatively through figures, quantitatively through tables, and by statistical tests of the residuals. The damped or periodical behaviors of the system’s solutions lead to their application on electronic circuits or other technological application fields.