Meshless symplectic and multi-symplectic scheme for the coupled nonlinear Schrödinger system based on local RBF approximation. (15th March 2023)

• Record Type: Journal Article
• Authors: Zhang, Shengliang; Sun, Zhengjie; Kumar, Alpesh
• Is Part Of: Computers & mathematics with applications. Volume 134(2023)
• Page Start: 16
• Page End: 32
• Publication Date: 2023-03-15
• Subjects: Local RBF method -- Symplectic -- Multi-symplectic -- Nonlinear Schrödinger system; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.12.018
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, a new meshless symplectic and multi-symplectic scheme is developed for solving the coupled nonlinear Schrödinger system. The key feature of the method is the utilization of local radial basis function (RBF) approximation (LRBFA) method in spatial discretization. The LRBFA only requires solving a small linear system, thus it can circumvent the ill-conditioned problem and shape-parameter-sensitivity of global RBF method. The proposed method offers a high order of convergence and conserves the invariants well. Various numerical examples are presented to verify that the proposed method is valid for both uniform knots and random knots.