On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation.
G.D. Akrivis, V.A. Dougalis, ... (1991)
Numerische Mathematik
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Displaying similar documents to “On the Steps of Convergence of Approximate Eigenvectors in the Rayleigh-Schrödinger Series.”
On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation.
Higher Order Convergence Results for the Rayleigh-Ritz Method Applied to Eigenvalue Problems: 2. Improved Error Bounds for Eigenfunctions.
R.S. Varga, J.G. Pierce (1972)
Numerische Mathematik
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On the convergence rate of the conjugate gradients in presence of rounding errors.
Yvan Notay (1993)
Numerische Mathematik
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Numerical study of self-focusing solutions to the Schrödinger-Debye system
Christophe Besse, Brigitte Bidégaray (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. Since the existence of blow-up solutions is an open problem, we try to compute such solutions. The convergence of the methods is proved and simulations seem indeed to show that for at least small delays self-focusing solutions may exist.
Bounds on resolvents of dilated Schrödinger operators with non trapping potentials
Pierre Duclos, Markus Klein (1985)
Journées équations aux dérivées partielles
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On the Convergence of the Galerkin Method for Nonsmooth Solutions of Integral Equations.
J. Saranen, K. Ruotsalainen (1989)
Numerische Mathematik
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Numerical aspects of the nonlinear Schrödinger equation in the semiclassical limit in a supercritical regime
Rémi Carles, Bijan Mohammadi (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
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We study numerically the semiclassical limit for the nonlinear Schrödinger equation thanks to a modification of the Madelung transform due to Grenier. This approach allows for the presence of vacuum. Even if the mesh size and the time step do not depend on the Planck constant, we recover the position and current densities in the semiclassical limit, with a numerical rate of convergence in accordance with the theoretical results, before shocks appear in the limiting Euler equation....