Conservative difference scheme for fractional Zakharov system and convergence analysis. Issue 7 (3rd July 2021)

• Record Type: Journal Article
• Authors: Shi, Yao; Ma, Qiang; Ding, Xiaohua
• Is Part Of: International journal of computer mathematics. Volume 98:Issue 7(2021)
• Page Start: 1474
• Page End: 1494
• Publication Date: 2021-07-03
• Subjects: Fractional Zakharov system -- conservative difference scheme -- high-order approximation -- convergence -- Riesz fractional derivative; 65M06 -- 65M12 -- 35Q51; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2020.1823973
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : In this paper, a high-accuracy conservative difference scheme is presented for solving the space fractional Zakharov system, which preserves the original conservative properties. By virtue of the standard energy method and mathematical induction, it is shown that the proposed scheme possesses the convergence rates of O ( τ 2 + h 4 ) . Finally, numerical examples testify the effectiveness of the conservative difference scheme and demonstrate the correctness of theoretical results. In particular, the effects of the fractional order α and β on the solitary solution behaviours are shown clearly through many intuitionistic images.