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

Finite Elements in Analysis and Design - Tập 59 - Trang 28-34 - 2012
Leilei Wei1, Yinnian He1, Xindong Zhang2, Shaoli Wang1
1Center for Computational Geosciences, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, PR China
2College of Mathematics Sciences, Xinjiang Normal University, Urumqi 830054, PR China

Tài liệu tham khảo

Biazar, 2009, An approximation to the solution of telegraph equation by variational iteration method, Numer. Methods Partial Differential Equations, 25, 797, 10.1002/num.20373 Cowan, 1986, Quasi-soliton and other behaviour of the nonlinear cubic-quintic Schrödinger equation, Can. J. Phys., 64, 311, 10.1139/p86-054 Cockburn, 2001, Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids, SIAM J. Numer. Anal., 39, 264, 10.1137/S0036142900371544 Deng, 2008, Finite element method for the space and time fractional Fokker–Planck equation, SIAM J. Numer. Anal., 47, 204, 10.1137/080714130 Du, 2010, A compact difference scheme for the fractional diffusion-wave equation, Appl. Math. Model., 34, 2998, 10.1016/j.apm.2010.01.008 Liu, 2003, Time fractional advection dispersion equation, J. Comput. Appl. Math., 13, 233, 10.1007/BF02936089 Lin, 2007, Finite difference/spectral approximations for the time-fractional diffusion equation, J. Comput. Phys., 225, 1533, 10.1016/j.jcp.2007.02.001 Li, 2011, Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion, Comput. Math. Appl., 62, 855, 10.1016/j.camwa.2011.02.045 Momani, 2010, Analytical approximate solutions of the fractional convection–diffusion equation with nonlinear source term by He's homotopy perturbation method, Int. J. Comput. Math., 87, 1057, 10.1080/00207160903023581 Murio, 2008, Implicit finite difference approximation for time fractional diffusion equations, Comput. Math. Appl., 56, 1138, 10.1016/j.camwa.2008.02.015 Naber, 2004, Time fractional Schröinger equation, J. Math. Phys., 45, 3339, 10.1063/1.1769611 Podlubny, 2002, Geometric and physical interpretation of fractional integration and fractional differentiation, Fract. Calc. Appl. Anal., 5, 367 Rida, 2008, On the solution of the fractional nonlinear Schröinger equation, Phys. Lett. A, 372, 553, 10.1016/j.physleta.2007.06.071 Yildirim, 2009, An algorithm for solving the fractional nonlinear Schröinger equation by means of the homotopy perturbation method, Int. J. Nonlinear Sci. Numer. Simul., 10, 445, 10.1515/IJNSNS.2009.10.4.445 Yildirim, 2010, He's homotopy perturbation method for solving the space and time fractional telegraph equations, Int. J. Comput. Math., 87, 2998, 10.1080/00207160902874653 Yildirim, 2009, Homotopy perturbation method for solving the space–time fractional advection–dispersion equation, Adv. Water Resour., 32, 1711, 10.1016/j.advwatres.2009.09.003