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A new high-order accurate conservative finite difference scheme for the coupled nonlinear Schr\”odinger equations
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  • Yuyu He,
  • X.F. Wang,
  • Weizhong dai,
  • YaQing Deng
Yuyu He
Minnan Normal University
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X.F. Wang
Henan Institute of Science and Technology
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Weizhong dai
Louisiana Tech University
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YaQing Deng
Minnan Normal University
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Peer review status:UNDER REVIEW

04 Jul 2020Submitted to Mathematical Methods in the Applied Sciences
10 Jul 2020Assigned to Editor
10 Jul 2020Submission Checks Completed
18 Jul 2020Reviewer(s) Assigned

Abstract

In this paper, a fourth-order accurate conservative finite difference scheme for solving the coupled nonlinear Schr\”odinger (CNLS) equations is proposed. Conservation of the discrete energy and masses, priori estimates, existence and uniqueness of numerical solutions, convergence with second-order in time and fourth-order in space as well as stability of the present scheme are proved by discrete energy method. A convergent iterative method for the present scheme is developed. Numerical experiments are given to support the theoretical analysis.