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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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[1] G.D. Akrivis, Finite difference discretization of the cubic Schrodinger equation, IMAJ. Numer. Anal. 13 (1993), 115–124. [2] W.Z. Bao, S. Jin and P.A. Markowich Numerical study of time -splitting spectral discretization of nonlinear Schrodinger equations in the semi classical regimes, SIAMJ. Sci. Comput. 25 (2003), 27–64. [3] Q.S. Chang, E.Jia and W. Sun: Difference schemes for solving the generalized nonlinear Schrodinger equation, J. Comput .Phys., 148(1999), 397-415. [4] M. Dehghan and A. Taleei, Numerical solution of nonlinear Schrodinger equation by using time-space pseudo -spectral method, Numer. Meth. Partial Differ. Equ. 26 (2010), 979–992. [5] X.L. HU and L.M. ZHANG, Conservative compact difference schemes for the coupled nonlinear Schrodinger system, Numer. Meth. Partial Differ. Eq. 30 (2014), 749-772 . [6] J.C. Jin, N. Wei and H.M. Zhang, A two-grid finite -element method for the nonlinear Schrodinger equation, J. Comput. Math. 33 (2015), 146–157. [7] H. A. Kashkool, and A.H. Aneed, Full-discrete weak Galerkin finite element method for solving diffusion - convection problem, J. Adv. Math. 13 (2017), no. 4, 7333–7344. [8] Y. LIU and H. LI, H1 -Galerkin mixed finite element method for the linear Schrodinger equation, ADV. Math. 39 (2010), 429–442. [9] V. Thomee, Galerkin finite element method for parabolic problems, (Springer Series in Computational Mathematics ), NJ, 1984.[10] J. Wang ,Y. Huang. : Fully discrete Galerkin finite element method for cubic nonlinear Schrodinger equation, Numer. Math. Teor. Meth. Appl. 10 (2017), no. 3, 671–688. [11] J. P. Wang, and X. Ye, :A weak Galerkin finite element method for second-order elliptic problems, J. Comput. Appl. Math. 241 (2013), no. 1, 103–115. [12] H.M. Zhang, J.C. Jin and J.Y. Wang, Two-grid finite -element method for the two -dimensional time -dependent Schrodinger equation, ADV. APPI. Math. Mech. 5 (2013), 180–193. [13] Y.M. Zhao, D.Y. Shi and F.Wang, High accuracy analysis of a new mixed finite element method for nonlinear Schrodinger equation, Math. Numer. Sin. 37 (2015), 162–177. | ||
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