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Compact Local Structure-Preserving Algorithms for the Nonlinear Schrödinger Equation with Wave Operator

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  • Langyang Huang
  • Zhaowei Tian
  • Yaoxiong Cai

Abstract

Combining the compact method with the structure-preserving algorithm, we propose a compact local energy-preserving scheme and a compact local momentum-preserving scheme for the nonlinear Schrödinger equation with wave operator (NSEW). The convergence rates of both schemes are . The discrete local conservative properties of the presented schemes are derived theoretically. Numerical experiments are carried out to demonstrate the convergence order and local conservation laws of the developed algorithms.

Suggested Citation

  • Langyang Huang & Zhaowei Tian & Yaoxiong Cai, 2020. "Compact Local Structure-Preserving Algorithms for the Nonlinear Schrödinger Equation with Wave Operator," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, January.
    • Handle: RePEc:hin:jnlmpe:4345278
    DOI: 10.1155/2020/4345278
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    Cited by:

    1. Yang, Yuna & Li, Hongwei & Guo, Xu, 2021. "A linearized energy-conservative scheme for two-dimensional nonlinear Schrödinger equation with wave operator," Applied Mathematics and Computation, Elsevier, vol. 404(C).

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