Raising the order of geometric numerical integrators by composition and extrapolation
type: Item
instance of: scholarly article
title: Raising the order of geometric numerical integrators by composition and extrapolation
zbMATH Open document ID: 1093.65070
author: Sergio Blanes
author: Fernando Casas
published in: Numerical Algorithms
publication date: 2005-04-25T00:00:00Z
review text: This paper deals with the construction of high order geometric integrators up to order sixteen. First, composition techniques are studied, the standard case, where one or more low order basic methods are composed, and the processing case, where one basic method of moderate order is composed with a post-processor method. Then the extrapolation technique for geometric integrators is analyzed. In general, the extrapolation doesn't preserve the geometric properties of the exact solution, but for most practical purposes, the preservation of the geometric properties they provide is sufficiently accurate. The interest of the integration schemes thus constructed is illustrated on the important class of differential equations \(y''=g(y,t)\) and the Schrödinger equation. Finally, several numerical examples are given.
reviewed by: Rudolf Scherer
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A26
Mathematics Subject Classification ID: 34L40
zbMATH DE Number: 2161200
zbMATH Keywords: geometric integration
zbMATH Keywords: composition methods
zbMATH Keywords: processing
zbMATH Keywords: extrapolation
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: s11075-004-5884-y
OpenAlex ID: W2097568771
cites work: Pseudo-symplectic Runge-Kutta methods
cites work: High order numerical integrators for differential equations using composition and processing of low order methods
cites work: On the Numerical Integration of Ordinary Differential Equations by Processed Methods
cites work: Composition Methods for Differential Equations with Processing
cites work: Symplectic Integration with Processing: A General Study
cites work: Extrapolation of symplectic integrators
cites work: High-order Runge-Kutta-Nyström geometric methods with processing
cites work: Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods
cites work: A symplectic integration algorithm for separable Hamiltonian functions
cites work: Extrapolation of symplectic methods for Hamiltonian problems
cites work: Symplectic integrators from composite operator factorizations
cites work: Q4531870
cites work: Solving Ordinary Differential Equations I
cites work: Composition constants for raising the orders of unconventional schemes for ordinary differential equations
cites work: Explicit Symplectic Integrators Using Hessian--Vector Products
cites work: On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods
cites work: Families of high-order composition methods
cites work: Splitting methods
cites work: Optimized Forest-Ruth- and Suzuki-like algorithms for integration of motion in many-body systems
cites work: A numerical algorithm for Hamiltonian systems
cites work: Hybrid exponential product formulas for unbounded operators with possible applications to Monte Carlo simulations
cites work: Q4527707
DOI: 10.1007/S11075-004-5884-Y
description: scientific article; zbMATH DE number 2161200