Unconditionally stable sixth-order structure-preserving scheme for the nonlinear Schrödinger equation with wave operator

Shuaikang Wang, Yongbin Ge and Sheng-en Liu

Applied Mathematics and Computation, 2025, vol. 498, issue C

Abstract: A structure-preserving two-level numerical method with sixth-order in both time and space is proposed for solving the nonlinear Schrödinger equation with wave operator. By introducing auxiliary variables to transform the original equation into a system, structure-preserving high-order difference scheme is obtained by applying the Crank-Nicolson method and the sixth-order difference operators for discretizing time and space derivatives. Subsequently, the conservation laws of energy and mass for the discretized solution produced by the established scheme are rigorously proven. And a theoretical analysis shows that the scheme is unconditionally convergent and stable in the L2-norm. Additionally, a corresponding fast solving algorithm is designed for the established scheme. And the Richardson extrapolation technique is used to enhance the temporal accuracy to sixth order. Finally, the effectiveness of the numerical scheme and the theoretical results of this study are validated through numerical experiments. The results also fully demonstrate the efficiency of the novel scheme in numerical computations.

Keywords: Nonlinear Schrödinger equation with wave operator; Structure-preserving; Convergence and stability; Fast solving algorithm; Richardson extrapolation technique (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:498:y:2025:i:c:s0096300325001195

DOI: 10.1016/j.amc.2025.129392

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