Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
Copyright policy )Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
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. \textit{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.
difference schemes, 35Q, NLS equations (nonlinear Schrödinger equations), splitting methods, 65M12, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], 510, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Lieformula, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, nonlinear Schrödinger equation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
difference schemes, 35Q, NLS equations (nonlinear Schrödinger equations), splitting methods, 65M12, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], 510, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Lieformula, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, nonlinear Schrödinger equation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
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