Abstract: The standard methods of perturbative analysis are crucial to revealing many features of a physical system when it is not viable to obtain exact solutions. Nevertheless, the use of a truncated expansion might generate diverging solutions in systems that are known to be bound. Following the perspective of secular perturbation theory, we propose the numerical implementation of a renormalization group-based approach to promote the background parameters into time-dependent quantities. These new quantities are not restricted only to avoid secular growth, but can also improve the accuracy of the solution. As a concrete example, we use this method to calculate the soliton-like solutions of the Korteweg-de Vries equation deformed by adding a small damping term. This example shares several features with the evaluation of gravitational waveforms modified by perturbative corrections of general relativity.
Numerical renormalization group-based approach to secular perturbation theory
Tomas Galvez (CITA) // November 25, 2020
Abstract: The standard methods of perturbative analysis are crucial to revealing many features of a physical system when it is not viable to obtain exact solutions. Nevertheless, the use of a truncated expansion might generate diverging solutions in systems that are known to be bound. Following the perspective of secular perturbation theory, we propose the numerical implementation of a renormalization group-based approach to promote the background parameters into time-dependent quantities. These new quantities are not restricted only to avoid secular growth, but can also improve the accuracy of the solution. As a concrete example, we use this method to calculate the soliton-like solutions of the Korteweg-de Vries equation deformed by adding a small damping term. This example shares several features with the evaluation of gravitational waveforms modified by perturbative corrections of general relativity.