Analysis of an implicit fully discrete local discontinuous Galerkin method for the time-fractional Schrödinger equation

Finite Elements in Analysis and Design ◽

10.1016/j.finel.2012.03.008 ◽

2012 ◽

Vol 59 ◽

pp. 28-34 ◽

Author(s):

Leilei Wei ◽

Yinnian He ◽

Xindong Zhang ◽

Shaoli Wang

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Fractional Schrödinger Equation ◽

Fully Discrete ◽

Local Discontinuous Galerkin ◽

Fractional Schrodinger Equation

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Mean-square convergence of a symplectic local discontinuous Galerkin method applied to stochastic linear Schrödinger equation

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drw023 ◽

2016 ◽

pp. drw023

Author(s):

Chuchu Chen ◽

Jialin Hong ◽

Lihai Ji

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Mean Square ◽

Local Discontinuous Galerkin ◽

Mean Square Convergence

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A conservative local discontinuous Galerkin method for the solution of nonlinear Schrödinger equation in two dimensions

Science China Mathematics ◽

10.1007/s11425-016-9118-x ◽

2017 ◽

Vol 60 (12) ◽

pp. 2515-2530 ◽

Author(s):

RongPei Zhang ◽

XiJun Yu ◽

MingJun Li ◽

XiangGui Li

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Nonlinear Schrödinger Equation ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Schrodinger Equation ◽

Two Dimensions ◽

Local Discontinuous Galerkin

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The WKB Local Discontinuous Galerkin Method for the Simulation of Schrödinger Equation in a Resonant Tunneling Diode

Journal of Scientific Computing ◽

10.1007/s10915-008-9237-1 ◽

2008 ◽

Vol 40 (1-3) ◽

pp. 360-374 ◽

Author(s):

Wei Wang ◽

Chi-Wang Shu

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Resonant Tunneling ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Resonant Tunneling Diode ◽

Local Discontinuous Galerkin ◽

Tunneling Diode

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A fully discrete local discontinuous Galerkin method for one-dimensional time-fractional Fisher's equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2013.866233 ◽

2014 ◽

Vol 91 (9) ◽

pp. 2021-2038 ◽

Author(s):

Xindong Zhang ◽

Yinnian He ◽

Leilei Wei ◽

Bo Tang ◽

Shaoli Wang

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

One Dimensional ◽

Fisher’S Equation ◽

Fully Discrete ◽

Local Discontinuous Galerkin ◽

Fisher's Equation

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Analysis of the fractional Kawahara equation using an implicit fully discrete local discontinuous Galerkin method

Numerical Methods for Partial Differential Equations ◽

10.1002/num.21756 ◽

2012 ◽

Vol 29 (5) ◽

pp. 1441-1458 ◽

Author(s):

Leilei Wei ◽

Yinnian He ◽

Bo Tang

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Kawahara Equation ◽

Fully Discrete ◽

Local Discontinuous Galerkin

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Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the fractional diffusion-wave equation

Numerical Algorithms ◽

10.1007/s11075-014-9827-y ◽

2014 ◽

Vol 67 (4) ◽

pp. 845-862 ◽

Author(s):

Huiya Dai ◽

Leilei Wei ◽

Xindong Zhang

Keyword(s):

Wave Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Numerical Algorithm ◽

Local Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Diffusion Wave ◽

Fully Discrete ◽

Local Discontinuous Galerkin

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A Fully-Discrete Local Discontinuous Galerkin Method for Convection-Dominated Sobolev Equation

Journal of Scientific Computing ◽

10.1007/s10915-011-9498-y ◽

2011 ◽

Vol 51 (1) ◽

pp. 107-134 ◽

Author(s):

Qiang Zhang ◽

Fuzheng Gao

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Sobolev Equation ◽

Fully Discrete ◽

Local Discontinuous Galerkin ◽

Convection Dominated

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A numerical study based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional coupled Schrödinger system

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2012.07.004 ◽

2012 ◽

Vol 64 (8) ◽

pp. 2603-2615 ◽

Author(s):

Leilei Wei ◽

Xindong Zhang ◽

Sunil Kumar ◽

Ahmet Yildirim

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Numerical Study ◽

Local Discontinuous Galerkin Method ◽

Fully Discrete ◽

Local Discontinuous Galerkin ◽

Coupled Schrödinger System ◽

Schrödinger System

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Optimal error estimate of conservative local discontinuous Galerkin method for nonlinear Schrödinger equation

Applied Numerical Mathematics ◽

10.1016/j.apnum.2018.01.004 ◽

2018 ◽

Vol 127 ◽

pp. 164-178 ◽

Author(s):

Jialin Hong ◽

Lihai Ji ◽

Zhihui Liu

Keyword(s):

Error Estimate ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Schrodinger Equation ◽

Optimal Error Estimate ◽

Optimal Error ◽

Local Discontinuous Galerkin

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Fully discrete local discontinuous Galerkin method for solving the fractional telegraph equation

CALCOLO ◽

10.1007/s10092-013-0084-6 ◽

2013 ◽

Vol 51 (1) ◽

pp. 175-192 ◽

Author(s):

Leilei Wei ◽

Huiya Dai ◽

Dingling Zhang ◽

Zhiyong Si

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Telegraph Equation ◽

Fully Discrete ◽

Local Discontinuous Galerkin ◽

Fractional Telegraph Equation

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