Symbolic calculation in development of algorithms : Split-step methods for the Gross-Pitaevskii equation

Javanainen, J. and Ruostekoski, J. (2006) Symbolic calculation in development of algorithms : Split-step methods for the Gross-Pitaevskii equation. Journal of Physics A: Mathematical and General, 39 (12). L179-L184. ISSN 0305-4470

Abstract

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