Split-step Fourier methods for the Gross-Pitaevskii equation

TL;DR

This paper systematically evaluates the accuracy of split-step Fourier methods for solving the time-dependent Gross-Pitaevskii equation, highlighting that using the latest wave function approximation results in consistent error order across algorithms.

Contribution

It provides a symbolic calculation-based analysis showing that all tested split-step Fourier methods have similar error order when the wave function is updated properly.

Findings

All split-step Fourier methods have the same error order under proper wave function updates.

Using the latest wave function approximation in the nonlinear potential is crucial for accuracy.

The study offers a systematic framework for assessing numerical methods for the Gross-Pitaevskii equation.

Abstract

We perform a systematic study of the accuracy of split-step Fourier transform methods for the time dependent Gross-Pitaevskii equation using symbolic calculation. Provided the most recent approximation for the wave function is always used in the nonlinear atom-atom interaction potential energy, every split-step algorithm we have tried has the same-order time stepping error for the Gross-Pitaevskii equation and the Schroedinger equation.