Numerical Simulation of the Coupled Sine-Gordon Equations via a Linearized and Decoupled Compact ADI Method. (4th July 2019)

• Record Type: Journal Article
• Authors: Deng, Dingwen
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 9(2019)
• Page Start: 1053
• Page End: 1079
• Publication Date: 2019-07-04
• Subjects: Convergence -- coupled sine-Gordon equations -- HOC ADI method -- solvability; 65M06; 65M12; 65M15.; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1596951
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: This article focuses on the development and analysis of a high-order compact (HOC) alternating direction implicit (ADI) method for solving a two-dimensional (2D) coupled sine-Gordon equations, which combines fourth-order compact difference for the approximations of the second spatial derivatives, Crank–Nicolson (C–N) method for temporal discretization and the approximation factorization of difference operators. By the discrete energy analysis method, it is shown that their solutions converge to the exact solutions with an order of two in time and four in space in L 2 -, H 1, and L ∞ -norms. Meanwhile, it is pointed out that the present method can be slightly adapted to the numerical solutions of other types of sine-Gordon equations, for example, sine-Gordon equation, doubled sine-Gordon equation, and damped wave equations. Finally, numerical findings testify the computational efficiency of the algorithms.