Galerkin finite element method for nonlinear fractional Schrödinger equations (Q509644)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Galerkin finite element method for nonlinear fractional Schrödinger equations |
scientific article; zbMATH DE number 6686466
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Galerkin finite element method for nonlinear fractional Schrödinger equations |
scientific article; zbMATH DE number 6686466 |
Statements
Galerkin finite element method for nonlinear fractional Schrödinger equations (English)
0 references
17 February 2017
0 references
The authors use the Crank-Nicolson scheme in time and the finite element method in space to solve a class of nonlinear Riesz space-fractional Schrödinger equations. Using a Brouwer fixed point theorem and a fractional Gagliardo-Nirenberg inequality, unique solvability of fully discrete systems is proved. The conservation and convergence properties of the semi-discrete scheme and the fully discrete one are analyzed. A linearized iterative finite element algorithm is introduced and some numerical examples are given to support the theoretical results.
0 references
nonlinear fractional Schrödinger equation
0 references
finite element method
0 references
Crank-Nicolson method
0 references
conservation
0 references
unique solvability
0 references
convergence
0 references
semidiscretization
0 references
numerical examples
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
