A meshless symplectic method for two-dimensional Schrödinger equation with radial basis functions

In this study we propose a meshless symplectic algorithm for two-dimensional time-dependent Schrödinger equation with radial basis functions (RBFs) approximation theory. The truncation error and global error are also investigated. The numerical experiments show that the scheme is higher-order accuracy, easy to implement with the scattered knots. Furthermore, the algorithm possesses a long-time tracking capability.