Conservative difference scheme for fractional Zakharov system and convergence analysis

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 $\mathcal{O}({\tau }^2+h^4)$. 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 α and β on the solitary solution behaviours are shown clearly through many intuitionistic images.

KEYWORDS:

• Fractional Zakharov system
• conservative difference scheme
• high-order approximation
• convergence
• Riesz fractional derivative

2010 Mathematics Subject Classifications:

• 65M06
• 65M12
• 35Q51

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Key R&D Program of China [No. 2017YFC1405600], the National Natural Science Foundation of China [Nos. 11501150 and 11701124], and the Natural Science Foundation of Shandong Province of China [No. ZR2017PA006].