High Order Stable Finite Difference Methods for the Schrödinger Equation
نویسندگان
چکیده
منابع مشابه
High Order Stable Finite Difference Methods for the Schrödinger Equation
In this paper we extend the Summation–by–parts–simultaneous approximation term (SBP–SAT) technique to the Schrödinger equation. Stability estimates are derived and the accuracy of numerical approximations of interior order 2m, m = 1, 2, 3, are analyzed in the case of Dirichlet boundary conditions. We show that a boundary closure of the numerical approximations of order m lead to global accuracy...
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Article history: Received 5 December 2013 Received in revised form 26 August 2014 Accepted 28 August 2014 Available online 6 September 2014
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In this work we present a general approach for developing high-order compact differencing schemes by utilizing the governing differential equation to help approximate truncation error terms. As an illustrative application we consider the stream-function vorticity form of the Navier Stokes equations, and provide driven cavity results. Some extensions to treat non-constant metric coefficients res...
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We establish uniform error estimates of finite difference methods for the nonlinear Schrödinger equation (NLS) perturbed by the wave operator (NLSW) with a perturbation strength described by a dimensionless parameter ε (ε ∈ (0, 1]). When ε → 0+, NLSW collapses to the standard NLS. In the small perturbation parameter regime, i.e., 0 < ε 1, the solution of NLSW is perturbed from that of NLS with ...
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ژورنال
عنوان ژورنال: Journal of Scientific Computing
سال: 2012
ISSN: 0885-7474,1573-7691
DOI: 10.1007/s10915-012-9628-1