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

Leilei Wei; Xindong Zhang; Sunil Kumar; Ahmet Yildirim

doi:10.1016/j.camwa.2012.07.004

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

Leilei Wei
, Xindong Zhang
, Sunil Kumar
, Ahmet Yildirim

Xi'an Jiaotong University
Xinjiang Normal University
National Institute of Technology Jamshedpur
Ege University

Research output: Contribution to journal › Article › peer-review

64 Scopus citations

Abstract

In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for solving the time-fractional coupled Schrödinger system. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. Through analysis we show that our scheme is unconditionally stable, and the L ² error estimate has the convergence rate O(hk+ ¹+(Δ t ²+( ^Δt)α2hk+ ¹²) for the linear case. Extensive numerical results are provided to demonstrate the efficiency and accuracy of the scheme.

Original language	English
Pages (from-to)	2603-2615
Number of pages	13
Journal	Computers and Mathematics with Applications
Volume	64
Issue number	8
DOIs	https://doi.org/10.1016/j.camwa.2012.07.004
State	Published - Oct 2012
Externally published	Yes

Keywords

Error estimates
Local discontinuous Galerkin method
Stability
Time-fractional coupled Schrödinger system

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10.1016/j.camwa.2012.07.004

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title = "A numerical study based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional coupled Schr{\"o}dinger system",

abstract = "In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for solving the time-fractional coupled Schr{\"o}dinger system. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. Through analysis we show that our scheme is unconditionally stable, and the L 2 error estimate has the convergence rate O(hk+ 1+(Δ t 2+( Δt)α2hk+ 12) for the linear case. Extensive numerical results are provided to demonstrate the efficiency and accuracy of the scheme.",

keywords = "Error estimates, Local discontinuous Galerkin method, Stability, Time-fractional coupled Schr{\"o}dinger system",

author = "Leilei Wei and Xindong Zhang and Sunil Kumar and Ahmet Yildirim",

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T1 - A numerical study based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional coupled Schrödinger system

AU - Wei, Leilei

AU - Zhang, Xindong

AU - Kumar, Sunil

AU - Yildirim, Ahmet

PY - 2012/10

Y1 - 2012/10

N2 - In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for solving the time-fractional coupled Schrödinger system. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. Through analysis we show that our scheme is unconditionally stable, and the L 2 error estimate has the convergence rate O(hk+ 1+(Δ t 2+( Δt)α2hk+ 12) for the linear case. Extensive numerical results are provided to demonstrate the efficiency and accuracy of the scheme.

AB - In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for solving the time-fractional coupled Schrödinger system. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. Through analysis we show that our scheme is unconditionally stable, and the L 2 error estimate has the convergence rate O(hk+ 1+(Δ t 2+( Δt)α2hk+ 12) for the linear case. Extensive numerical results are provided to demonstrate the efficiency and accuracy of the scheme.

KW - Error estimates

KW - Local discontinuous Galerkin method

KW - Stability

KW - Time-fractional coupled Schrödinger system

UR - https://www.scopus.com/pages/publications/84866729748

U2 - 10.1016/j.camwa.2012.07.004

DO - 10.1016/j.camwa.2012.07.004

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SN - 0898-1221

VL - 64

SP - 2603

EP - 2615

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 8

ER -

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

Abstract

Keywords

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