Conservative compact difference scheme for the Zakharov–Rubenchik equations. Issue 3 (4th March 2019)

• Record Type: Journal Article
• Authors: Ji, Bingquan; Zhang, Luming; Zhou, Xuanxuan
• Is Part Of: International journal of computer mathematics. Volume 96:Issue 3(2019)
• Page Start: 537
• Page End: 556
• Publication Date: 2019-03-04
• Subjects: Zakharov–Rubenchik equations -- induction argument -- compact difference scheme -- conservation laws -- convergence; 65M06 -- 35Q51; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2018.1437261
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this article, a compact difference scheme is investigated to solve the Zakharov–Rubenchik equations in one dimension. The new scheme is proved to conserve the total mass and energy in the discrete sense. Rigorous error estimates are established for the new method with the help of an induction argument in energy space which show that the new scheme has second-order accuracy in time and fourth-order accuracy in space. Extensive numerical results are provided to verify our theoretical analysis, and show the accuracy and efficiency of the new scheme.