Conservative difference scheme for fractional Zakharov system and convergence analysis

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(tau(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 alpha and beta on the solitary solution behaviours are shown clearly through many intuitionistic images.

Automated summary

This paper introduces a high-accuracy conservative difference scheme for solving the space fractional Zakharov system, with proven convergence rates. Numerical examples show the effectiveness of the scheme and validate theoretical results, highlighting the effects of fractional orders alpha and beta on solitary solution behaviors through intuitive images.