application of moving kriging interpolation based on the meshless local petrov-galerkin (mk-mlpg) method for the two-dimensional time-dependent schrodinger equation

In this article, an eficient numerical technique for solving the twodimensional time-dependent schrodinger equation is presented. at first, we employ the meshless local petrov-galerkin (mlpg) method based on a local weak formulation to construct a system of discretized equations and then the solution of time-dependent schrodinger equation will be approximated. we use the moving kriging (mk) interpolation instead of moving least square (mls) approximation to construct the mlpg shape functions and hence the heaviside step function is chosen as a test function on each subdomain. in this method, no mesh is needed neither for integration of the local weak form nor construction of the shape functions. so, the mlpg is truly a meshless method. several numerical examples are presented and the results are compared to their analytical and rbf solutions to illustrate the accuracy and capability of this algorithm.