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

•Systematic construction of novel meshless multi-symplectic method for the “good” Boussinesq equation.•Multi-symplectic integrators based on local radial basis function (RBF) collocation method (LRBFCM).•Discrete energy conservation and momentum conservation with a negligible error.•Meshless character and high-order approximation property of the method.•Overcoming the problems of ill-conditioning and shape parameter sensitivity of the global RBF collocation method. 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 only a 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.