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.

这项工作为 Klein-Gordon-Schrödinger 系统提出了一种新颖的无网格辛和多辛近似。该方法的主要特点是： （一）局部径向基函数（RBF）搭配法（LRBFCM）在空间离散化中的应用；(二)辛积分器在时间离散化中的应用。LRBFCM方法可以解决全局RBF方法的病态问题和形状参数敏感性问题，简单有效。讨论了该方法的保守性并评估了其准确性。对具有规则和不规则域的一维 (1D)/2D 进行了数值模拟，以验证我们新方法的有效性。