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Discrete transparent boundary conditions for the Schrodinger equation -- a compact higher order scheme
| 1. | Institut für Angewandte und Numerische Mathematik, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, 48149 Münster, Germany |
| 2. | Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstr. 8, 1040 Wien, Australia |
| [1] |
Bernard Ducomet, Alexander Zlotnik, Ilya Zlotnik. On a family of finite-difference schemes with approximate transparent boundary conditions for a generalized 1D Schrödinger equation. Kinetic & Related Models, 2009, 2 (1) : 151-179. doi: 10.3934/krm.2009.2.151 |
| [2] |
Alexander Zlotnik, Ilya Zlotnik. Finite element method with discrete transparent boundary conditions for the time-dependent 1D Schrödinger equation. Kinetic & Related Models, 2012, 5 (3) : 639-667. doi: 10.3934/krm.2012.5.639 |
| [3] |
Takeshi Fukao, Shuji Yoshikawa, Saori Wada. Structure-preserving finite difference schemes for the Cahn-Hilliard equation with dynamic boundary conditions in the one-dimensional case. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1915-1938. doi: 10.3934/cpaa.2017093 |
| [4] |
Claire david@lmm.jussieu.fr David, Pierre Sagaut. Theoretical optimization of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 286-293. doi: 10.3934/proc.2007.2007.286 |
| [5] |
Gianluca Frasca-Caccia, Peter E. Hydon. Locally conservative finite difference schemes for the modified KdV equation. Journal of Computational Dynamics, 2019, 6 (2) : 307-323. doi: 10.3934/jcd.2019015 |
| [6] |
Emma Hoarau, Claire david@lmm.jussieu.fr David, Pierre Sagaut, Thiên-Hiêp Lê. Lie group study of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 495-505. doi: 10.3934/proc.2007.2007.495 |
| [7] |
Adam M. Oberman. Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian. Discrete & Continuous Dynamical Systems - B, 2008, 10 (1) : 221-238. doi: 10.3934/dcdsb.2008.10.221 |
| [8] |
Roumen Anguelov, Jean M.-S. Lubuma, Meir Shillor. Dynamically consistent nonstandard finite difference schemes for continuous dynamical systems. Conference Publications, 2009, 2009 (Special) : 34-43. doi: 10.3934/proc.2009.2009.34 |
| [9] |
Jiaxiang Cai, Juan Chen, Bin Yang. Fully decoupled schemes for the coupled Schrödinger-KdV system. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5523-5538. doi: 10.3934/dcdsb.2019069 |
| [10] |
Lih-Ing W. Roeger. Dynamically consistent discrete Lotka-Volterra competition models derived from nonstandard finite-difference schemes. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 415-429. doi: 10.3934/dcdsb.2008.9.415 |
| [11] |
Marcel Braukhoff, Ansgar Jüngel. Entropy-dissipating finite-difference schemes for nonlinear fourth-order parabolic equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020234 |
| [12] |
Raimund Bürger, Kenneth H. Karlsen, John D. Towers. On some difference schemes and entropy conditions for a class of multi-species kinematic flow models with discontinuous flux. Networks & Heterogeneous Media, 2010, 5 (3) : 461-485. doi: 10.3934/nhm.2010.5.461 |
| [13] |
Olivier Goubet, Ezzeddine Zahrouni. On a time discretization of a weakly damped forced nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2008, 7 (6) : 1429-1442. doi: 10.3934/cpaa.2008.7.1429 |
| [14] |
Frank Wusterhausen. Schrödinger equation with noise on the boundary. Conference Publications, 2013, 2013 (special) : 791-796. doi: 10.3934/proc.2013.2013.791 |
| [15] |
César Augusto Bortot, Wellington José Corrêa, Ryuichi Fukuoka, Thales Maier Souza. Exponential stability for the locally damped defocusing Schrödinger equation on compact manifold. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1367-1386. doi: 10.3934/cpaa.2020067 |
| [16] |
Lassaad Aloui, Imen El Khal El Taief. The Kato smoothing effect for the nonlinear regularized Schrödinger equation on compact manifolds. Mathematical Control & Related Fields, 2019 doi: 10.3934/mcrf.2020016 |
| [17] |
Qi Hong, Jialing Wang, Yuezheng Gong. Second-order linear structure-preserving modified finite volume schemes for the regularized long wave equation. Discrete & Continuous Dynamical Systems - B, 2019, 24 (12) : 6445-6464. doi: 10.3934/dcdsb.2019146 |
| [18] |
Yones Esmaeelzade Aghdam, Hamid Safdari, Yaqub Azari, Hossein Jafari, Dumitru Baleanu. Numerical investigation of space fractional order diffusion equation by the Chebyshev collocation method of the fourth kind and compact finite difference scheme. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020402 |
| [19] |
Katherine A. Kime. Palindromic control and mirror symmetries in finite difference discretizations of 1-D Schrödinger equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1601-1621. doi: 10.3934/dcdsb.2018063 |
| [20] |
Weizhu Bao, Chunmei Su. Uniform error estimates of a finite difference method for the Klein-Gordon-Schrödinger system in the nonrelativistic and massless limit regimes. Kinetic & Related Models, 2018, 11 (4) : 1037-1062. doi: 10.3934/krm.2018040 |
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