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\begin{document}

\title{On the meshless quasi-interpolation methods for solving 2D sine-Gordon
equations}



\author[1]{Li Shanshan}%
\author[1]{Yong DUAN}%
\author[1]{Libing Bai}%
\affil[1]{University of Electronic Science and Technology of China}%


\vspace{-1em}



  
  \date{June 05, 2024}


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\begin{abstract}
This paper is devoted to applying a numerical method for solution of the
2D sine-Gordon equation. The bivariate multiple quadratic
quasi-interpolation ( MQQI ) method is adopted to simulate this
equations, which the first order spatial derivative is approximated by
MQQI, the second spatial and time derivative are approximated by forward
difference. One of the merit of this scheme is its simple structure and
easy implementation. In the meanwhile, we present truncation and total
error of this scheme, high accuracy and efficiency of the method are
verified by numerical experiments. In addition, the optimal value of
parameters are investigated in this article based on Luh {[}10, 11{]}.%
\end{abstract}%



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