Barycentric Lagrange interpolation collocation method for solving the Sine-Gordon equation

This paper mainly discusses the numerical solution of Sine-Gordon (SG) equation which is widely used in engineering field. Different from the classical numerical calculation method, we choose the barycentric Lagrange interpolation collocation method (BLICM) to solve the SG equation. Firstly, the barycentric Lagrange interpolation is introduced and its differential matrix is given. Secondly, two linearized iterative schemes namely direct linearized iterative scheme and Newton linearized iterative scheme to solve SG equation are constructed, the matrix equation of the two iterative scheme is obtained. Thirdly, the Newton-Raphson iterative scheme for SG equation is also presented and the detailed solution process is given. Finally, several numerical examples with exact solution are given to show the accuracy of BLICM, the results of three iterative schemes with equidistant nodes and Chebyshev nodes are compared. Further, some examples with line and ring solitons are given to simulate by BLICM, the accurate numerical results are obtained to support our experiments.(c) 2023 Elsevier B.V. All rights reserved.