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Galerkin finite element method for nonlinear fractional Schrödinger equations.
- Source :
-
Numerical Algorithms . Feb2017, Vol. 74 Issue 2, p499-525. 27p. - Publication Year :
- 2017
-
Abstract
- In this paper, a class of nonlinear Riesz space-fractional Schrödinger equations are considered. Based on the standard Galerkin finite element method in space and Crank-Nicolson difference method in time, the semi-discrete and fully discrete systems are constructed. By Brouwer fixed point theorem and fractional Gagliardo-Nirenberg inequality, we prove the fully discrete system is uniquely solvable. Moreover, we focus on a rigorous analysis and consideration of the conservation and convergence properties for the semi-discrete and fully discrete systems. Finally, a linearized iterative finite element algorithm is introduced and some numerical examples are given to confirm the theoretical results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10171398
- Volume :
- 74
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Numerical Algorithms
- Publication Type :
- Academic Journal
- Accession number :
- 120846355
- Full Text :
- https://doi.org/10.1007/s11075-016-0160-5