Optimal stability polynomials for splitting methods, with application to the time-dependent Schrödinger equation
type: Item
instance of: scholarly article
title: Optimal stability polynomials for splitting methods, with application to the time-dependent Schrödinger equation
zbMATH Open document ID: 0888.65095
DOI: 10.1016/S0168-9274(97)00064-0
author: Stephen K. Gray
author: Robert I. McLachlan
published in: Applied Numerical Mathematics
publication date: 1998-06-04T00:00:00Z
review text: The authors determine optimal stability polynomials for the splitting method to solve systems of ordinary differential equations, accurate to the eighth order in the time step. The method is applied to the construction of symplectic corrector algorithms which approximate the solutions of linear Hamiltonian systems. As an illustration, the authors examine the discretized form of the time-dependent Schrödinger equation which can be reduced to a Hamiltonian system and describes the time evolution of a particle in a certain one-dimensional potential.
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 1088834
zbMATH Keywords: optimal stability polynomials
zbMATH Keywords: splitting method
zbMATH Keywords: symplectic corrector algorithms
zbMATH Keywords: linear Hamiltonian systems
zbMATH Keywords: time-dependent Schrödinger equation
zbMATH Keywords: one-dimensional potential
MaRDI profile type: Publication
cites work: Q5577991
cites work: Q4878826
cites work: On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods
cites work: Q4343693
cites work: The accuracy of symplectic integrators
cites work: Generating functions for dynamical systems with symmetries, integrals, and differential invariants
cites work: Q5289008
cites work: Q4315882
cites work: Q4343698
full work available at URL: s0168-9274(97)00064-0
OpenAlex ID: W2083260836
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description: scientific article; zbMATH DE number 1088834