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

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Published 8 March 2006 • 2006 IOP Publishing Ltd
, , Citation Juha Javanainen and Janne Ruostekoski 2006 J. Phys. A: Math. Gen. 39 L179 DOI 10.1088/0305-4470/39/12/L02

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Author affiliations

1 Department of Physics, University of Connecticut, Storrs, CT 06269-3046, USA

2 School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK

Dates

  1. Received 24 January 2006
  2. Published

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0305-4470/39/12/L179

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 wavefunction 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 Schrödinger equation.

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10.1088/0305-4470/39/12/L02