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