On the necessity of negative coefficients for operator splitting schemes of order higher than two
type: Item
instance of: scholarly article
title: On the necessity of negative coefficients for operator splitting schemes of order higher than two
zbMATH Open document ID: 1071.65097
author: Sergio Blanes
author: Fernando Casas
published in: Applied Numerical Mathematics
publication date: 2005-06-01T00:00:00Z
review text: For an autonomous ordinary differential equation that is separable in solvable parts, operator splitting methods are known to be useful numerical tools. It is known that such methods must have negative coefficients if their order is \(\geq 3\). The authors give an instructive and elementary proof of this fact. The technique of the proof allows to draw useful additional conclusions about, e.g., the distribution of the negative coefficients. Moreover, examples are given showing that higher order schemes without negative coefficients exist for a slightly different class of differential equations.
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 2173598
zbMATH Keywords: operator splitting method
zbMATH Keywords: composition method
zbMATH Keywords: effective order
zbMATH Keywords: numerical integrator
zbMATH Keywords: Numerical examples
MaRDI profile type: Publication
full work available at URL: j.apnum.2004.10.005
OpenAlex ID: W2118185346
cites work: High order numerical integrators for differential equations using composition and processing of low order methods
cites work: Symplectic Integration with Processing: A General Study
cites work: On the Numerical Integration of Ordinary Differential Equations by Processed Methods
cites work: Q5577991
cites work: Q4343688
cites work: Fourth-order symplectic integration
cites work: Nth-Order Operator Splitting Schemes and Nonreversible Systems
cites work: Q4531870
cites work: Q5687018
cites work: Explicit Symplectic Integrators Using Hessian--Vector Products
cites work: Explicit Lie-Poisson integration and the Euler equations
cites work: On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods
cites work: The accuracy of symplectic integrators
cites work: Splitting methods
cites work: Computations in a free Lie algebra
cites work: A numerical algorithm for Hamiltonian systems
cites work: Solving Linear Partial Differential Equations by Exponential Splitting
cites work: Chaotic Evolution of the Solar System
cites work: General theory of fractal path integrals with applications to many-body theories and statistical physics
cites work: Q4343698
DOI: 10.1016/J.APNUM.2004.10.005
description: scientific article; zbMATH DE number 2173598