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Order estimates in time of splitting methods for the nonlinear Schrödinger equation. (English) Zbl 1026.65073
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.

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
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