Back to Search
Start Over
Stability and error analysis for a second-order approximation of 1D nonlocal Schrodinger equation under D{\lowercase{t}}N-type boundary conditions.
- Source :
- Mathematics of Computation; Mar2022, Vol. 91 Issue 334, p761-783, 23p
- Publication Year :
- 2022
-
Abstract
- A second-order Crank-Nicolson finite difference method is designed to solve a 1D nonlocal Schrödinger equation on the whole real axis. We employ an asymptotically compatible scheme to discretize the spatially nonlocal operator, and apply the Crank-Nicolson scheme in time to achieve a fully discrete infinite system. An iterative technique for the second-order matrix difference equation is then developed to obtain Dirichlet-to-Dirichlet (DtD)-type artificial boundary conditions (ABCs) with the application of z-transform for the resulting fully discrete system. After that, with the aid of discrete nonlocal Green's first identity, we derive Dirichlet-to-Neumann (DtN)-type ABCs from DtD-type ABCs. The resulting DtN-type ABCs are available to reduce the infinite discrete system to a finite discrete system on a truncated computational domain, and make it possible to perform stability and convergence analysis for the reduced problem. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]
- Subjects :
- FINITE difference method
DISCRETE systems
DIFFERENCE equations
BEES algorithm
Subjects
Details
- Language :
- English
- ISSN :
- 00255718
- Volume :
- 91
- Issue :
- 334
- Database :
- Complementary Index
- Journal :
- Mathematics of Computation
- Publication Type :
- Academic Journal
- Accession number :
- 155211392
- Full Text :
- https://doi.org/10.1090/mcom/3685