A Modified Analytical Method for Solving Relativistic Oscillator

Abstract

In this study, we address the limitations of the conventional Modified Lindstedt-Poincare (MLP) method when applied to the nonlinear relativistic oscillator. Recognizing the inadequacies of the traditional approach, we propose a novel variant of the MLP method tailored specifically to tackle the complexities inherent in such systems. Our new method offers a robust framework for deriving approximate periodic solutions to the nonlinear relativistic oscillator. We rigorously compare the solutions generated by our method against exact solutions and those obtained using other established techniques. The comparative analysis demonstrates that our approach not only aligns closely with the exact solutions but also surpasses the accuracy of other existing methods. Furthermore, the proposed method is characterized by its simplicity and ease of implementation, making it a practical tool for solving strongly nonlinear oscillatory systems. The methodology introduced in this paper holds promise for broader applications and can be readily extended to address other strongly nonlinear oscillators, potentially paving the way for new insights and developments in the field.