Meshless symplectic and multi-symplectic algorithm for Klein–Gordon–Schrödinger system with local RBF collocation

Abstract

This work proposes a novel meshless symplectic and multi-symplectic approximation for Klein–Gordon–Schrödinger system. The main features of this method are: (I) the application of local radial basis function (RBF) collocation method (LRBFCM) in spatial discretization; (II) the application of symplectic integrator in time discretization. LRBFCM method can deal with the ill-conditioned problem and shape-parameter sensitivity of global RBF method, and is simple and effective. The conservatism of this method is discussed and its accuracy is evaluated. Numerical simulations are given for one dimension (1D)/2D with regular and irregular domains to verify the effectiveness of our new method.