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Application of moving kriging interpolation based on the meshless local Petrov-Galerkin (MK-MLPG) method for the two-dimensional time-dependent Schrodinger equation | ||
| Journal of Mahani Mathematical Research | ||
| مقاله 4، دوره 7، شماره 2، دی 2018، صفحه 105-125 اصل مقاله (732.24 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2019.12431.1063 | ||
| نویسندگان | ||
| Esmail Hesameddini* 1؛ Ali Habibirad2 | ||
| 1Department of Mathematical Sciences, Shiraz University of Technology, Shiraz, Iran | ||
| 2Department of Applied Mathematics Faculty of Basic Sciences, Shiraz University of Technology, shiraz, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Meshless local Petrov-Galerkin (MLPG) method؛ two-dimensional time-dependent Schrodinger equation؛ Moving Kriging interpolation | ||
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آمار تعداد مشاهده مقاله: 348 تعداد دریافت فایل اصل مقاله: 330 |
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