Numerical Solution of Shrödinger Equations Based on the Meshless Methods

In this work, two-dimensional time-dependent quantum equation problems are studied. We introduce a numerical algorithm for solving the two-dimensional nonlinear complex quantum system with MLS and FDM methods. An eﬃcient and accurate computational algorithm based on both, the moving least squares (MLS) and the ﬁnite diﬀerence (FDM) methods is proposed for solving it. The results demonstrate that the proposed algorithm is a robust algorithm with good accuracy. This is developed on MLS and FDM methods using numerical simulation for solving these kind of problems.