Discrete transparent boundary conditions for Schrödinger-type equations
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Publication:1360440
DOI10.1006/jcph.1997.5675zbMath0878.65111OpenAlexW2028858390MaRDI QIDQ1360440
Publication date: 12 January 1998
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/d74607d3bbae56baffdace185c77e792b754f886
Calculus of Mikusi?ski and other operational calculi (44A40) NLS equations (nonlinear Schrödinger equations) (35Q55) Applications to the sciences (65Z05)
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Cites Work
- Unnamed Item
- Absorbing boundaries for wave propagation problems
- Discrete transparent boundary conditions for the numerical solution of Fresnel's equation
- A pseudospectral Chebychev method for the 2D wave equation with domain stretching and absorbing boundary conditions
- Asymptotic Expansions and Boundary Conditions for Time-Dependent Problems
- Artificial Boundary Conditions for Incompletely Parabolic Perturbations of Hyperbolic Systems
- Absorbing Boundary Conditions for the Numerical Simulation of Waves
- Implementation of transparent boundaries for numerical solution of the Schröder equation.