Application of moving kriging interpolation based on the meshless local Petrov-Galerkin (MK-MLPG) method for the two-dimensional time-dependent Schrodinger equation

Abstract

‎In this article‎, ‎an efficient numerical technique for solving the two-dimensional time-dependent Schrodinger equation is presented‎. ‎At first‎, ‎we employ the meshless‎‎local Petrov-Galerkin (MLPG) method based on a local weak formulation to construct a system of discretized equations and then the solution of time-dependentSchrodinger‎equation will be approximated‎. ‎We use the Moving Kriging (MK) interpolation instead‎‎of Moving least Square (MLS) approximation to construct the MLPG shape functions‎‎and hence the Heaviside step function is chosen to be the test function‎. ‎In this method‎,‎no mesh is needed neither for integration of the local weak form nor construction of the‎‎shape functions‎. ‎So‎, ‎the MLPG is truly a meshless method‎. ‎Several numerical examples‎‎are presented and the results are compared to their analytical and RBF‎‎solutions to illustrate the accuracy and capability of this algorithm‎.

Keywords

• ‎meshless local petrov-galerkin (mlpg) method‎
• ‎two-dimensional time-dependent‎ ‎schrodinger equation‎
• ‎moving kriging interpolation