On the meshless quasi-interpolation methods for solving 2D sine-Gordon equations

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].