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Decoupled Crank-Nicolson LeapFrog Methods for the Evolution Boussinesq equations
  • Xiaofeng Jia,
  • Hui Feng
Xiaofeng Jia
Wuhan University

Corresponding Author:jiaxiaofeng@whu.edu.cn

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Hui Feng
Wuhan University
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Abstract

This paper presents decoupled second-order accurate algorithms based on Crank-Nicolson LeapFrog (CNLF) scheme for the evolution Boussinesq equations. The proposed algorithms deal with the spatial discretization by finite element method and treat the temporal discretization by CNLF method. For the nonlinear term in the Boussinesq equations, the semi-implicit method is used. Unconditional stability and error estimate of the numerical algorithm are proven. Some numerical tests are presented to justify the theoretical analysis.

Peer review status:ACCEPTED

07 Sep 2022Submitted to Mathematical Methods in the Applied Sciences
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08 Sep 2022Submission Checks Completed
08 Sep 2022Assigned to Editor
16 Sep 2022Reviewer(s) Assigned
07 Jan 2023Review(s) Completed, Editorial Evaluation Pending
07 Jan 2023Editorial Decision: Revise Minor
20 Feb 20231st Revision Received
20 Feb 2023Submission Checks Completed
20 Feb 2023Assigned to Editor
20 Feb 2023Review(s) Completed, Editorial Evaluation Pending
14 Mar 2023Reviewer(s) Assigned
23 Apr 2023Editorial Decision: Accept