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

WEI, Leilei; ZHANG, Xindong; KUMAR, Sunil; YILDIRIM, AHMET

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 Schrodinger system

Atıf İçin Kopyala

WEI L., ZHANG X., KUMAR S., YILDIRIM A.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, cilt.64, ss.2603-2615, 2012 (SCI İndekslerine Giren Dergi)

Cilt numarası: 64 Konu: 8
Basım Tarihi: 2012
Doi Numarası: 10.1016/j.camwa.2012.07.004
Dergi Adı: COMPUTERS & MATHEMATICS WITH APPLICATIONS
Sayfa Sayıları: ss.2603-2615

Özet

In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LOG) finite element method for solving the time-fractional coupled Schrodinger 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(h(k+1) + (Delta t)(2) + (Delta t)(alpha/2) h(k+1/2)) for the linear case. Extensive numerical results are provided to demonstrate the efficiency and accuracy of the scheme. (C) 2012 Elsevier Ltd. All rights reserved.