A flexible symplectic scheme for two-dimensional Schr\"{o}dinger equation with highly accurate RBFs quasi-interpolation

Abstract

Based on highly accurate multiquadric quasi-interpolation, this study suggests a meshless symplectic procedure for two-dimensional time-dependent Schr\"{o}dinger equation. The method is high-order accurate, flexible with respect to the geometry, computationally efficient and easy to implement. We also present a theoretical framework to show the conservativeness and convergence of the proposed method. As the numerical experiments show, it not only offers a high order accuracy but also has a good performance in the long time integration.