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<p>In this paper, we analyze the stability and convergence orders of the time-splitting schemes for the deterministic and stochastic Gross-Pitaevskii equations with rotating action in the Sobolev space. The whole process heavily depends on the integral representation. Firstly, we derive the computational properties of the Laplace operator and the angular momentum operator, and prove the second-order convergence of the Strang-type splitting scheme for the deterministic equation. Secondly, we introduce the truncated equation so that the nonlinear term is globally Lipschitz continuous. This makes it possible to prove the first-order convergence of the splitting method, and then extend the conclusion to the original stochastic equation. Finally, several numerical experiments are presented to support our theoretical findings.</p>

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Order of Convergence of Splitting Schemes for Deterministic/Stochastic Gross-Pitaevskii Equations with Rotating Angular Momentum

  • 期刊论文

  • 发表日期：

    2025年7月31日

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  • Rong Gao,
  • Jialin Hong,
  • Linghua Kong,
  • Songpei Ouyang,
  • Lan Wang

摘要

In this paper, we analyze the stability and convergence orders of the time-splitting schemes for the deterministic and stochastic Gross-Pitaevskii equations with rotating action in the Sobolev space. The whole process heavily depends on the integral representation. Firstly, we derive the computational properties of the Laplace operator and the angular momentum operator, and prove the second-order convergence of the Strang-type splitting scheme for the deterministic equation. Secondly, we introduce the truncated equation so that the nonlinear term is globally Lipschitz continuous. This makes it possible to prove the first-order convergence of the splitting method, and then extend the conclusion to the original stochastic equation. Finally, several numerical experiments are presented to support our theoretical findings.