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

سال انتشار: 1397
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 368

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شناسه ملی سند علمی:

JR_KJMMRC-7-2_004

تاریخ نمایه سازی: 5 خرداد 1398

چکیده مقاله:

‎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.

کلیدواژه ها:

‎Meshless local Petrov-Galerkin (MLPG) method‎ ، ‎two-dimensional time-dependent‎ ‎Schrodinger equation‎ ، ‎Moving Kriging interpolation

نویسندگان

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