RESEARCH ARTICLE
Maximum Convergence of a Novel High-Precision Conservative Compact Difference Scheme for the Coupled Nonlinear Schrödinger (CNLS) Equations
Shuguang Li,
Corresponding Author
Shuguang Li
School of Science, Dalian Maritime University, Dalian, China
Correspondence:
Shuguang Li ([email protected])
Search for more papers by this authorShuguang Li,
Corresponding Author
Shuguang Li
School of Science, Dalian Maritime University, Dalian, China
Correspondence:
Shuguang Li ([email protected])
Search for more papers by this authorFirst published: 01 July 2025
Funding: This work is supported by the “China Postdoctoral Science Foundation (No. 2023M740468)”, the “Natural Science Foundation of Liaoning Province in China (No. 2022-BS-093)”, the “Education Basic Research Project of Liaoning Province in China (No. JYTQN2023042)”, the “Fundamental Research Funds for the Central Universities (No. 3132024195, No. 3132023521)”.
ABSTRACT
In this work, a novel high-order compact conservative difference scheme for the coupled nonlinear Schrödinger (CNLS) equations is researched. The scheme is three-level nonlinear-implicit. The biggest novelty of the proposed scheme is that it adopts the averaging technique based on the classic Crank–Nicolson method, and it has discrete mass conservation and energy conservation. The numerical analysis of the proposed scheme is discussed by using the standard discrete energy method, the matrix energy technique, and the mathematical induction. Theoretical results show that the numerical solution converges unconditionally, and the optimal convergent rate is proved to be at in the discrete maximum norm with grid size and time step . Finally, numerical experiments verify the correctness of the theoretical results and demonstrate the efficiency and accuracy of the proposed scheme.
Open Research
Data Availability Statement
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
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