The renormalization group: A perturbation method for the graduate curriculum (Q2902840)

The paper is concerned with the applications of the renormalization group (RG) method to second-order ordinary differential equations with small regular perturbation terms in the form \(\epsilon \dot{y}\) or \(\epsilon y^3\), where \(\epsilon\rightarrow 0^+\).NEWLINENEWLINEThe RG method develops a mathematical apparatus that allows a systematic and unified investigation of the changes of a physical system viewed at different distance scales. In this paper, that method is considered in the context of a linear oscillator model and the standard Duffing oscillator with cubic nonlinearity and provides closed-form expressions for the amplitude via the renormalized expansion. Finally, the relation of the RG method to the method of multiple scales is discussed and some open problems are raised.