Besse, Christophe; Bidégaray, Brigitte; Descombes, Stéphane Order estimates in time of splitting methods for the nonlinear Schrödinger equation. (English) Zbl 1026.65073 SIAM J. Numer. Anal. 40, No. 1, 26-40 (2002). The nonlinear Schrödinger equation \[ u_t+ i\Delta u- F(u)= 0, \] for \(t> 0\) in two dimension and under the initial conditions \(u(x,0)= u_0(x)\) is investigated. By an operator-theoretic proof it is shown, that the Lie and Strang formulas for splitting [cf. G. Strang, ibid. 5, 506-517 (1968; Zbl 0184.38503)] are the approximations of the exact solution of the given equation, which are of the order 1 and 2 in time. Cited in 48 Documents MSC: 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35Q55 NLS equations (nonlinear Schrödinger equations) 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs Keywords:nonlinear Schrödinger equation; splitting methods; Lieformula; difference schemes PDF BibTeX XML Cite \textit{C. Besse} et al., SIAM J. Numer. Anal. 40, No. 1, 26--40 (2002; Zbl 1026.65073) Full Text: DOI