Coupled anharmonic oscillators: the Rayleigh-Ritz approach versus the collocation approach

TL;DR

This paper compares the convergence efficiency of the Rayleigh-Ritz method and a variational collocation approach for coupled anharmonic oscillators, demonstrating that RR achieves more accurate results with less computational effort.

Contribution

It provides a direct comparison between the Rayleigh-Ritz and collocation methods, highlighting the superior convergence and efficiency of the RR approach for this system.

Findings

Rayleigh-Ritz method converges monotonically

RR achieves higher accuracy at lower computational cost

Collocation approach is less efficient for coupled anharmonic oscillators

Abstract

For a system of coupled anharmonic oscillators we compare the convergence rate of the variational collocation approach presented recently by Amore and Fernandez (2010 Phys.Scr.81 045011) with the one obtained using the optimized Rayleigh-Ritz (RR) method. The monotonic convergence of the RR method allows us to obtain more accurate results at a lower computational cost.