Linearly Implicit Conservative Schemes for the Nonlocal Schrödinger Equation

Yutong Zhang, Bin Li () and Mingfa Fei
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Yutong Zhang: Applied Mathematics and Computational Science, School of Arts and Sciences, University of Pennsylvania, Philadelphia, PA 19104, USA
Bin Li: School of Science, Xuchang University, Xuchang 461000, China
Mingfa Fei: School of Mathematics, Changsha University, Changsha 410073, China

Mathematics, 2024, vol. 12, issue 21, 1-13

Abstract: This paper introduces two high-accuracy linearly implicit conservative schemes for solving the nonlocal Schrödinger equation, employing the extrapolation technique. These schemes are based on the generalized scalar auxiliary variable approach and the symplectic Runge–Kutta method. By integrating these advanced methods, the proposed schemes aim to significantly enhance computational accuracy and efficiency, while maintaining the essential conservative properties necessary for accurate physical modeling. This offers a structured approach to handle auxiliary variables, ensuring stability and conservation, while the symplectic Runge–Kutta method provides a robust framework with high accuracy. Together, these techniques offer a powerful and reliable approach for researchers dealing with complex quantum mechanical systems described by the nonlocal Schrödinger equation, ensuring both accuracy and stability in their numerical simulations.

Keywords: nonlocal Schrödinger equation; energy-preserving schemes; extrapolation technique; symplectic Runge–Kutta method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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