Unconditional and optimal H 2-error estimates of two linear and conservative finite difference schemes for the Klein-Gordon-Schrödinger equation in high dimensions

High Dimensions ◽

Klein Gordon

Coupling finite volume and nonstandard finite difference schemes for a singularly perturbed Schrödinger equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2015.1076569 ◽

2015 ◽

Vol 93 (11) ◽

pp. 1833-1844 ◽

Cited By ~ 5

Author(s):

A.A. Aderogba ◽

M. Chapwanya ◽

J. Djoko Kamdem ◽

J.M.-S. Lubuma

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Finite Volume ◽

Schrodinger Equation ◽

Difference Schemes ◽

Singularly Perturbed ◽

Nonstandard Finite Difference

Family of finite-difference schemes with approximate transparent boundary conditions for the generalized nonstationary Schrödinger equation in a semi-infinite strip

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542511030122 ◽

2011 ◽

Vol 51 (3) ◽

pp. 355-376 ◽

Cited By ~ 8

Author(s):

I. A. Zlotnik

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Difference Schemes ◽

Nonstationary Schrödinger Equation

Infinite Strip ◽

Transparent Boundary Conditions ◽

Lecture Notes in Computational Science and Engineering - Numerical Mathematics and Advanced Applications - ENUMATH 2013 ◽

Splitting in Potential Finite-Difference Schemes with Discrete Transparent Boundary Conditions for the Time-Dependent Schrödinger Equation

10.1007/978-3-319-10705-9_20 ◽

2014 ◽

pp. 203-211 ◽

Cited By ~ 1

Author(s):

Alexander Zlotnik ◽

Bernard Ducomet ◽

Ilya Zlotnik ◽

Alla Romanova

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Difference Schemes ◽

Time Dependent ◽

Transparent Boundary Conditions

Unconditional $$L^{\infty }$$ L ∞ -convergence of two compact conservative finite difference schemes for the nonlinear Schrödinger equation in multi-dimensions

CALCOLO ◽

10.1007/s10092-018-0277-0 ◽

2018 ◽

Vol 55 (3) ◽

Cited By ~ 2

Author(s):

Tingchun Wang ◽

Xiaofei Zhao

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Difference Schemes ◽

Nonlinear Schrödinger

Conservative finite difference schemes for the chiral nonlinear Schrödinger equation

Boundary Value Problems ◽

10.1186/s13661-015-0350-4 ◽

2015 ◽

Vol 2015 (1) ◽

Cited By ~ 3

Author(s):

Mohammad S Ismail ◽

Khalil S Al-Basyouni ◽

Ayhan Aydin

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Difference Schemes ◽

Nonlinear Schrödinger

Transparent boundary conditions for higher-order finite-difference schemes of the Schrödinger equation in (1+1)D

Computer Physics Communications ◽

10.1016/j.cpc.2019.107048 ◽

2020 ◽

Vol 250 ◽

pp. 107048 ◽

Cited By ~ 1

Author(s):

Mathias Schwendt ◽

Walter Pötz

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Higher Order ◽

Difference Schemes ◽

Transparent Boundary Conditions

Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2008.11.011 ◽

2009 ◽

Vol 198 (9-12) ◽

pp. 1052-1060 ◽

Cited By ~ 58

Author(s):

Shu-Sen Xie ◽

Guang-Xing Li ◽

Sucheol Yi

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

High Accuracy ◽

Difference Schemes ◽

Compact Finite Difference ◽

One Dimensional ◽

Compact Finite Difference Schemes

Family of finite-difference schemes with transparent boundary conditions for the nonstationary Schrödinger equation in a semi-infinite strip

Doklady Mathematics ◽

10.1134/s1064562411010066 ◽

2011 ◽

Vol 83 (1) ◽

pp. 12-18 ◽

Cited By ~ 4

Author(s):

A. A. Zlotnik ◽

I. A. Zlotnik

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Difference Schemes ◽

Nonstationary Schrödinger Equation

Infinite Strip ◽

Transparent Boundary Conditions ◽

Numerical stability of explicit Runge–Kutta finite-difference schemes for the nonlinear Schrödinger equation

Applied Numerical Mathematics ◽

10.1016/j.apnum.2013.04.002 ◽

2013 ◽

Vol 71 ◽

pp. 24-40 ◽

Cited By ~ 11

Author(s):

R.M. Caplan ◽

R. Carretero-González

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Numerical Stability ◽

Schrodinger Equation ◽

Difference Schemes ◽

Nonlinear Schrödinger ◽

Runge Kutta

Error estimates of a conservative finite difference Fourier pseudospectral method for the Klein–Gordon–Schrödinger equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2019.06.028 ◽

2020 ◽

Vol 79 (7) ◽

pp. 1956-1971 ◽

Cited By ~ 1

Author(s):

Bingquan Ji ◽

Luming Zhang

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Error Estimates ◽

Schrodinger Equation ◽

Pseudospectral Method ◽

Fourier Pseudospectral Method ◽

Klein Gordon ◽

Fourier Pseudospectral ◽

Difference Fourier