Order estimates in time of splitting methods for the nonlinear Schrödinger equation
Besse, Christophe ; Bidégaray, Brigitte ; Descombes, Stéphane
HAL, hal-00319991 / Harvested from HAL
Text on HAL
In this paper, we consider the nonlinear Schrödinger equation ut + iΔu − F(u) = 0 in two dimensions. We show, by an operator-theoretic proof, that the well-known Lie and Strang formulae (which are splitting methods) are approximations of the exact solution of order 1 and 2 in time.
Publié le : 2002-07-05
Classification:  splitting methods,  nonlinear Schrödinger equation,  65M12, 35Q,  [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] 
@article{hal-00319991,
     author = {Besse, Christophe and Bid\'egaray, Brigitte and Descombes, St\'ephane},
     title = {Order estimates in time of splitting methods for the nonlinear Schr\"odinger equation},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00319991}
}

Besse, Christophe; Bidégaray, Brigitte; Descombes, Stéphane. Order estimates in time of splitting methods for the nonlinear Schrödinger equation. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00319991/