scholarly journals Transparent Boundary Conditions for Time-Dependent Problems

2008 ◽  
Vol 30 (5) ◽  
pp. 2358-2385 ◽  
Author(s):  
Daniel Ruprecht ◽  
Achim Schädle ◽  
Frank Schmidt ◽  
Lin Zschiedrich
Keyword(s):  
Boundary Conditions ◽  
Time Dependent ◽  
Transparent Boundary Conditions ◽  
Time Dependent Problems

High-accurate transparent boundary conditions for time-dependent quantum wave packet method

2020 ◽  
Vol 33 (2) ◽  
pp. 258-262 ◽  
Author(s):  
Yin Huang ◽  
Hai-lin Zhao ◽  
Syed Kazim Usman ◽  
Ganiyu Ayodele Ajibade ◽  
Zhi-gang Sun
Keyword(s):  
Wave Packet ◽  
Boundary Conditions ◽  
Time Dependent ◽  
Transparent Boundary Conditions ◽  
Quantum Wave

scholarly journals Derivation of boundary conditions for the artificial boundaries associated with the solution of certain time dependent problems by Lax–Wendroff type difference schemes

1982 ◽  
Vol 25 (1) ◽  
pp. 1-18 ◽  
Author(s):  
John C. Wilson
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Time Dependent ◽  
Finite Region ◽  
Partial Differential ◽  
Artificial Boundaries ◽  
Fixed Boundaries ◽  
Time Dependent Problems

Many problems involving the solution of partial differential equations require the solution over a finite region with fixed boundaries on which conditions are prescribed. It is a well known fact that the numerical solution of many such problems requires additional conditions on these boundaries and these conditions must be chosen to ensure stability. This problem has been considered by, amongst others, Kreiss [11, 12, 13], Osher [16, 17], Gustafsson et al. [9] Gottlieb and Tarkel [7] and Burns [1]

Remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schrödinger equation on the half-axis

2016 ◽  
Vol 31 (1) ◽  
Author(s):  
Alexander Zlotnik ◽  
Ilya Zlotnik
Keyword(s):  
Finite Difference ◽  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Finite Difference Schemes ◽  
Transparent Boundary Conditions ◽  
Space Step ◽  
Half Axis ◽  
Generalized Time

AbstractWe consider the generalized time-dependent Schrödinger equation on the half-axis and a broad family of finite-difference schemes with the discrete transparent boundary conditions (TBCs) to solve it. We first rewrite the discrete TBCs in a simplified form explicit in space step

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