[1] |
DELFOUR M, FORTIN M, PAYRE G. Finite-difference solutions of a non-linear Schrdinger equation[J]. Journal of Computational Physics,1981,44(2): 277-288.
|
[2] |
EBAID A, KHALED S M. New types of exact solutions for nonlinear Schrdinger equation with cubic nonlinearity[J]. Journal of Computational and Applied Mathematics,2011,235(8): 1984-1992.
|
[3] |
LI B Y, SUN W W. Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations[J]. International Journal of Numerical Analysis and Modeling,2013,10(3): 622-633.
|
[4] |
LI B Y, SUN W W. Unconditionally optimal error estimates of a Crank-Nicolson Galerkin method for the nonlinear thermistor equations[J]. SIAM Journal on Numerical Analysis,2012,52(2): 933-954.
|
[5] |
LAMBERT J D. Numerical Methods for Ordinary Differential Systems: the Initial Value Problem [J]. New York: John Wiley & Sons Inc, 1991.
|
[6] |
BAKER G, DOUGALIS V, KARAKASHIAN O. On a higher accurate fully discrete Galerkin approximation to the Navier-Stokes equations[J]. Mathematics of Computation,1982,39(160): 339-375.
|
[7] |
CAI W, LI J, CHEN Z. Unconditional convergence and optimal error estimates of the Euler semi-implicit scheme for a generalized nonlinear Schrdinger equation[J]. Advances in Computational Mathematics,2016,42(6): 1311-1330.
|
[8] |
CAI W, LI J, CHEN Z. Unconditional optimal error estimates for BDF2-FEM for a nonlinear Schrdinger equation[J]. Journal of Computational and Applied Mathematics,2018,331: 23-41.
|
[9] |
DUPONT T. Three-level Galerkin methods for parabolic equations[J]. SIAM Journal on Numerical Analysis,1974,11(2): 392-410.
|
[10] |
姜礼尚, 庞之垣. 有限元方法及其理论[M]. 北京: 人民教育出版社, 1979.(JIANG Lishang, PANG Zhiyuan. Finite Element Method and Its Theory [M]. Beijing: People’s Education Press, 1979.(in Chinese))
|
[11] |
BREZZI F, RAPPAZ J, RAVIART P A. Finite Dimensional Approximation of Nonlinear Problems [M]. New York: Springer-Verlag, 1980.
|
[12] |
AKRIVIS G, LARSSON S. Linearly implicit finite element methods for the time-dependent Joule heating problem[J]. Bit Numerical Mathematics,2005,45(3): 429-442.
|
[13] |
JENSEN M, MALQVIST A. Finite element convergence for the Joule heating problem with mixed boundary conditions[J]. Bit Numerical Mathematics,2013, 53(2): 475-496.
|
[14] |
BULUT H, PANDIR Y, DEMIRAY S T. Exact solutions of nonlinear Schrdinger equation with dual power-law nonlinearity by extended trial equation method[J]. Waves Random Complex Media,2014,24(4): 439-451.
|
[15] |
HEYWOOD J G, RANNACHER R. Finite element approximation of the nonstationary Navier-Stokes problem IV: error analysis for second-order time discretization[J]. SIAM Journal on Numerical Analysis,1984,27(2): 353-384.
|
[16] |
FEIT M D, FLECK J A, STEIGER A. Solution of the Schrdinger equation by a spectral method II: vibrational energy levels of triatomic molecules[J]. Journal of Computational Physics,1983,78(1): 301-308.
|