2009
DOI: 10.1016/j.apnum.2009.02.002
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Exponential Runge–Kutta methods for the Schrödinger equation

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Cited by 37 publications
(46 citation statements)
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“…x is a linear isometry in H r (see (6)) the error in u and v is the same, i.e., u(t n ) − u n r = v(t n ) − v n r . Thanks to the representations (34), (35) and the form of the remainder R 2γ (τ 1+2γ ) given in (11) we obtain with the help of Lemma 3.1 that…”
Section: Convergence Analysis In One Dimension (D = 1)mentioning
confidence: 99%
“…x is a linear isometry in H r (see (6)) the error in u and v is the same, i.e., u(t n ) − u n r = v(t n ) − v n r . Thanks to the representations (34), (35) and the form of the remainder R 2γ (τ 1+2γ ) given in (11) we obtain with the help of Lemma 3.1 that…”
Section: Convergence Analysis In One Dimension (D = 1)mentioning
confidence: 99%
“…Our goal in this paper is to introduce and analyse two classes of exponential methods for the time integration of (1.1) on a d-dimensional space. The first class is that of exponential Runge-Kutta methods [37,38,27]. The second class relies on the Lawson techniques [43,45].…”
Section: Introductionmentioning
confidence: 99%
“…The RK4-IP method can be interpreted as an exponential Runge-Kutta method according to the general form presented in [24] for the semi-linear parabolic problems, but this method is not of collocation type as studied in [23] for parabolic problems and in [13] for the Schrödinger equation.…”
Section: Presentation Of the Numerical Approachmentioning
confidence: 99%