Application of moving kriging interpolation based on the meshless local Petrov-Galerkin (MK-MLPG) method for the two-dimensional time-dependent Schrodinger equation
Publish place: Journal of Mahani Mathematical Research، Vol: 7، Issue: 2
Publish Year: 1397
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_KJMMRC-7-2_004
تاریخ نمایه سازی: 5 خرداد 1398
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
Authors
Esmail Hesameddini
Department of Mathematical Sciences, Shiraz University of Technology, Shiraz, Iran
ali Habibirad
Department of Applied Mathematics Faculty of Basic Sciences, Shiraz University of Technology, shiraz, Iran
Khadijeh Abolpour
Department of Mathematics Shiraz Branch, Islamic Azad University Shiraz, Iran