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Weak Galerkin finite element method for the nonlinear Schrodinger equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 198، دوره 13، شماره 2، مهر 2022، صفحه 2453-2468 اصل مقاله (721.85 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27518.3634 | ||
| نویسندگان | ||
| Dalal Ismael Aziz؛ Ahmed J. Hussein* | ||
| College of Education for Pure Sciences, University of Thi-Qar, Iraq | ||
| تاریخ دریافت: 13 دی 1400، تاریخ بازنگری: 30 بهمن 1400، تاریخ پذیرش: 21 اسفند 1400 | ||
| چکیده | ||
| The numerical technique for a two-dimensional time-dependent nonlinear Schrodinger equation is the subject of this work. The approximations are produced using the weak Galerkin finite element technique with semi-discrete and fully discrete finite element methods, respectively, using the backward Euler method and the crank-Nicolson method in time. Using the elliptic projection operator, we provide optimum $L^{2}$ error estimates for semi and fully discrete weak Galerkin finite elements. Finally, we present numerical examples provided to verify our theoretical results. | ||
| کلیدواژه‌ها | ||
| WGFEM؛ nonlinear Schrodinger equation؛ semi-discrete؛ Fully discrete (backward Euler scheme؛ Crank-Nicolson scheme)؛ error estimates | ||
| مراجع | ||
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