作者：Shengliang Zhang

题名：A meshless multi-symplectic local radial basis function collocation scheme for the “good” Boussinesq equation

期刊：Applied Mathematics and Computation 431 (2022) 127297

摘要：A novel meshless multi-symplectic scheme is proposed for the “good” Boussinesq equation.The scheme consists of a local radial basis function (RBF) collocation method (LRBFCS) in space and a symplectic integrator in time. The LRBFCS is simple and efficient, since onlya sparse banded linear system has to be solved. Moreover, it can avoid the ill-conditioned problem and shape-parameter-sensitivity of the global RBF method. The multi-symplectic LRBFCS (MLRBFCS) is more accurate than traditional methods. Numerical experiments with uniform knots and random knots are designed to verify the effectiveness of the method.