A fast Strang splitting method with mass conservation for the space-fractional Gross-Pitaevskii equation

Yao-Yuan Cai and Hai-Wei Sun

Applied Mathematics and Computation, 2024, vol. 470, issue C

Abstract: In this paper, we present a fast algorithm for solving the space-fractional Gross-Pitaevskii equation while preserving the law of mass conservation. First we discretize this equation by using a second-order weighted and shifted Grünward difference operator and obtain a system of semilinear differential equations with linear and nonlinear parts. Afterwards, we employ a Strang splitting method to solve this semi-discretization scheme. To further reduce computational time, we propose a two-level Strang splitting method from the linear part. This method significantly reduces computational complexity to O(nlog⁡n) by implementing the fast Fourier transform. Importantly, our proposed method ensures the unconditional preservation of mass conservation and achieves second-order convergence. At last, we demonstrate the validity of our approach through numerical experiments and graphical results presented.

Keywords: Fractional Gross–Pitaevskii equation; Circulant and skew-circulant matrix exponential; Two-level Strang splitting method; Mass conservation; Fast Fourier transform (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:470:y:2024:i:c:s009630032400047x

DOI: 10.1016/j.amc.2024.128575

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