Krylov subspace spectral methods for the time-dependent Schrödinger equation with non-smooth potentials
type: Item
instance of: scholarly article
title: Krylov subspace spectral methods for the time-dependent Schrödinger equation with non-smooth potentials
zbMATH Open document ID: 1168.65055
author: James Lambers
published in: Numerical Algorithms
publication date: 2009-06-30T00:00:00Z
review text: This paper presents modifications of Krylov subspace spectral (KSS) methods, which build on the work of Gene Golub and others pertaining to moments and Gaussian quadrature to produce high-order accurate approximate solutions to the time-dependent Schrödinger equation in the case where either the potential energy or the initial data is not a smooth function. These modifications consist of using various symmetric perturbations to compute off-diagonal elements of functions of matrices. It is demonstrated through analytical and numerical results that KSS methods, with these modifications, achieve the same high-order accuracy and possess the same stability properties as they do when applied to parabolic problems, even though the solutions to the Schrödinger equation do not possess the same smoothness.
reviewed by: Wilhelm Heinrichs
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 5571642
zbMATH Keywords: Spectral methods
zbMATH Keywords: Gaussian quadrature
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: variable coefficient
zbMATH Keywords: Lanczos method
zbMATH Keywords: Krylov subspace method
zbMATH Keywords: numerical results
zbMATH Keywords: stability
describes a project that uses: Matlab
describes a project that uses: Ode15s
describes a project that uses: ode113
describes a project that uses: ode23s
describes a project that uses: MATLAB ODE suite
describes a project that uses: ode23
describes a project that uses: ode45
MaRDI profile type: Publication
full work available at URL: s11075-009-9278-z
OpenAlex ID: W2133719542
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DOI: 10.1007/S11075-009-9278-Z
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description: scientific article; zbMATH DE number 5571642