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

Hesameddini, Esmail; Habibirad, Ali

doi:10.22103/jmmrc.2019.12431.1063

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

Document Type : Research Paper

Authors

Esmail Hesameddini ¹

Ali Habibirad ²

¹ Department of Mathematical Sciences, Shiraz University of Technology, Shiraz, Iran

² Department of Applied Mathematics Faculty of Basic Sciences, Shiraz University of Technology, shiraz, Iran

10.22103/jmmrc.2019.12431.1063

Abstract

‎In this article‎, ‎an efficient numerical technique for solving the two-dimensional 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-dependentSchrodinger
‎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 to be the test function‎. ‎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.

Keywords

‎Meshless local Petrov-Galerkin (MLPG) method‎

‎two-dimensional time-dependent‎ ‎Schrodinger equation‎

‎Moving Kriging interpolation