This study presents an innovative non-perturbative approach (NPA) to analyze the damped Mathieu cubic–quintic Duffing oscillator, a nonlinear parametric oscillatory system with applications in various fields such as optics, quantum physics, and general relativity. The NPA transforms the nonlinear ordinary differential equation (ODE) into a linear equation, allowing for the derivation of approximate solutions without relying on traditional perturbation methods. This approach is particularly effective for both small and large amplitude parametric oscillations, offering high numerical precision and practicality. The study demonstrates that the NPA can rapidly estimate the frequency-amplitude relationship, enabling successive approximations of the solutions for parametric nonlinear fluctuations. The derived parametric equation is validated against the original equation, showing high agreement. Stability analysis is conducted in multiple scenarios, and Floquet theory is used to examine transition curves. The NPA is characterized by its clear principles, making it user-friendly and capable of achieving high numerical precision. It is particularly beneficial for addressing nonlinear parametric problems due to its ability to minimize algebraic complexity during implementation. The method is applied to analyze the nonlinear cubic–quintic Duffing Mathieu oscillator, providing a novel solution for both frequency and phase space solutions of parametric oscillations. The study also explores the effects of damping and parametric excitation on the system's behavior. The frequency formula is derived considering the presence of damping and parametric excitation, showing that the NPA can accurately approximate the system's response. Stability analysis is performed for different parameters, revealing how changes in parameters affect the system's stability. The results show that the NPA provides accurate solutions with minimal error, validating its effectiveness in analyzing nonlinear parametric oscillations. The method is applied to various cases, including special cases where the excitation frequency equals the natural frequency, and the effects of different parameters on the system's stability are analyzed. The study concludes that the NPA is a powerful and efficient technique for analyzing nonlinear parametric oscillations, offering a practical solution for complex dynamical systems.This study presents an innovative non-perturbative approach (NPA) to analyze the damped Mathieu cubic–quintic Duffing oscillator, a nonlinear parametric oscillatory system with applications in various fields such as optics, quantum physics, and general relativity. The NPA transforms the nonlinear ordinary differential equation (ODE) into a linear equation, allowing for the derivation of approximate solutions without relying on traditional perturbation methods. This approach is particularly effective for both small and large amplitude parametric oscillations, offering high numerical precision and practicality. The study demonstrates that the NPA can rapidly estimate the frequency-amplitude relationship, enabling successive approximations of the solutions for parametric nonlinear fluctuations. The derived parametric equation is validated against the original equation, showing high agreement. Stability analysis is conducted in multiple scenarios, and Floquet theory is used to examine transition curves. The NPA is characterized by its clear principles, making it user-friendly and capable of achieving high numerical precision. It is particularly beneficial for addressing nonlinear parametric problems due to its ability to minimize algebraic complexity during implementation. The method is applied to analyze the nonlinear cubic–quintic Duffing Mathieu oscillator, providing a novel solution for both frequency and phase space solutions of parametric oscillations. The study also explores the effects of damping and parametric excitation on the system's behavior. The frequency formula is derived considering the presence of damping and parametric excitation, showing that the NPA can accurately approximate the system's response. Stability analysis is performed for different parameters, revealing how changes in parameters affect the system's stability. The results show that the NPA provides accurate solutions with minimal error, validating its effectiveness in analyzing nonlinear parametric oscillations. The method is applied to various cases, including special cases where the excitation frequency equals the natural frequency, and the effects of different parameters on the system's stability are analyzed. The study concludes that the NPA is a powerful and efficient technique for analyzing nonlinear parametric oscillations, offering a practical solution for complex dynamical systems.