A variational sinc collocation method for strong-coupling problems

TL;DR

The paper introduces a variational sinc collocation method that efficiently solves strong-coupling problems like Schrödinger equations and lattice models, achieving high accuracy with limited computational effort.

Contribution

It presents a novel variational sinc collocation approach that provides exponential error reduction for strong-coupling problems, improving computational efficiency and precision.

Findings

Errors decrease exponentially with grid points

High precision achieved with limited numerical effort

Applicable to linear, nonlinear, and lattice models

Abstract

We have devised a variational sinc collocation method (VSCM) which can be used to obtain accurate numerical solutions to many strong-coupling problems. Sinc functions with an optimal grid spacing are used to solve the linear and non-linear Schr\"odinger equations and a lattice $\phi^4$ model in $(1+1)$. Our results indicate that errors decrease exponentially with the number of grid points and that a limited numerical effort is needed to reach high precision.