High Order Stable Finite Difference Methods for the Schrödinger Equation

Journal of Scientific Computing ◽

10.1007/s10915-012-9628-1 ◽

2012 ◽

Vol 55 (1) ◽

pp. 173-199 ◽

Author(s):

A. Nissen ◽

G. Kreiss ◽

M. Gerritsen

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Finite Difference Methods ◽

Difference Methods

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Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator

SIAM Journal on Numerical Analysis ◽

10.1137/110830800 ◽

2012 ◽

Vol 50 (2) ◽

pp. 492-521 ◽

Author(s):

Weizhu Bao ◽

Yongyong Cai

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Error Estimates ◽

Wave Operator ◽

Schrodinger Equation ◽

Finite Difference Methods ◽

Nonlinear Schrodinger Equation ◽

Uniform Error ◽

Difference Methods ◽

Uniform Error Estimates

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Absorption of waves by complex surface layers in the solution of the Schrödinger equation by finite difference methods

Computer Physics Communications ◽

10.1016/0010-4655(83)90091-7 ◽

1983 ◽

Vol 30 (3) ◽

pp. 243-247 ◽

Author(s):

Norbert Grün ◽

Werner Scheid

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Finite Difference Methods ◽

Complex Surface ◽

Surface Layers ◽

Difference Methods

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On finite difference methods for the solution of the Schrödinger equation

Computers & Chemistry ◽

10.1016/s0097-8485(99)00023-6 ◽

1999 ◽

Vol 23 (6) ◽

pp. 513-554 ◽

Author(s):

T.E. Simos ◽

P.S. Williams

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Finite Difference Methods ◽

Difference Methods

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Uniform point-wise error estimates of semi-implicit compact finite difference methods for the nonlinear Schrödinger equation perturbed by wave operator

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2014.08.026 ◽

2015 ◽

Vol 422 (1) ◽

pp. 286-308 ◽

Author(s):

Tingchun Wang

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Error Estimates ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Finite Difference Methods ◽

Nonlinear Schrodinger Equation ◽

Compact Finite Difference ◽

Difference Methods

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Solving the nonlinear Schrödinger equation using cubic B-spline interpolation and finite difference methods

10.1063/1.4995862 ◽

2017 ◽

Author(s):

Azhar Ahmad ◽

Amirah Azmi ◽

Ahmad Abd. Majid ◽

Nur Nadiah Abd Hamid

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Spline Interpolation ◽

Finite Difference Methods ◽

Nonlinear Schrodinger Equation ◽

B Spline ◽

Nonlinear Schrödinger ◽

Difference Methods

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Solving the nonlinear Schrödinger equation using cubic B-spline interpolation and finite difference methods on dual solitons

10.1063/1.4980908 ◽

2017 ◽

Author(s):

Azhar Ahmad ◽

Amirah Azmi ◽

Ahmad Abd. Majid ◽

Nur Nadiah Abd Hamid

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Spline Interpolation ◽

Finite Difference Methods ◽

Nonlinear Schrodinger Equation ◽

B Spline ◽

Nonlinear Schrödinger ◽

Difference Methods

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High order finite difference methods for unsteady incompressible flows in multi-connected domains

Computers & Fluids ◽

10.1016/s0045-7930(03)00037-9 ◽

2004 ◽

Vol 33 (2) ◽

pp. 223-255 ◽

Author(s):

Jian-Guo Liu ◽

Cheng Wang

Keyword(s):

Finite Difference ◽

Incompressible Flows ◽

Finite Difference Methods ◽

Difference Methods ◽

High Order Finite Difference

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A review of high-order and optimized finite-difference methods for simulating linear wave phenomena

10.2514/6.1997-2088 ◽

1997 ◽

Author(s):

D. Zingg ◽

D. Zingg

Keyword(s):

Finite Difference ◽

Finite Difference Methods ◽

Linear Wave ◽

Difference Methods ◽

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On the spurious solutions in the high-order finite difference methods for eigenvalue problems

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2007.06.018 ◽

2007 ◽

Vol 196 (49-52) ◽

pp. 5031-5046 ◽

Author(s):

S. Zhao

Keyword(s):

Finite Difference ◽

Eigenvalue Problems ◽

Finite Difference Methods ◽

Spurious Solutions ◽

Difference Methods ◽

High Order Finite Difference

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High-order finite difference methods for a second order dual-phase-lagging models of microscale heat transfer

Applied Mathematics and Computation ◽

10.1016/j.amc.2017.03.035 ◽

2017 ◽

Vol 309 ◽

pp. 31-48 ◽

Author(s):

Dingwen Deng ◽

Yaolin Jiang ◽

Dong Liang

Keyword(s):

Heat Transfer ◽

Finite Difference ◽

Finite Difference Methods ◽

Second Order ◽

Microscale Heat Transfer ◽

Difference Methods ◽

High Order Finite Difference

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