题名: Meshless Symplectic and Multi-symplectic Local RBF Collocation Methods for Hamiltonian PDEs

期刊：Journal of Scientific Computing  ，2021（88）

摘要:This study presents a novel meshless symplectic and multi-symplectic local radial basis function (RBF) collocation method (LRBFCM) for Hamiltonian partial differential equations. Specifically, the nonlinear wave equation and nonlinear Schrödinger equation are considered. The discretization in space is based on LRBFCM and then in time by symplectic integrator. The conservativeness of the method is explored and the accuracy is assessed. The LRBFCM is simple and efficient, since it can avoid the ill-conditioned problem and shape-parametersensitivity of global RBF method. Numerical experiments with uniform knots and random knots are designed to illustrate the effectiveness of the method.