Composition Methods for Dynamical Systems Separable into Three Parts

Composition Methods for Dynamical Systems Separable into Three Parts

New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a way that each part is explicitly solvable. The methods are...

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Main Authors: Fernando Casas, Alejandro Escorihuela-Tomàs
Format: Article
Language:English
Published: MDPI AG 2020-04-01
Series:Mathematics
Subjects:
composition methods
splitting methods
systems separable into three parts
geometric numerical integrators
Online Access:https://www.mdpi.com/2227-7390/8/4/533
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spelling doaj-8e4dac4d69b74830bf9ad6cda1be08012020-11-25T02:21:57ZengMDPI AGMathematics2227-73902020-04-01853353310.3390/math8040533Composition Methods for Dynamical Systems Separable into Three PartsFernando Casas0Alejandro Escorihuela-Tomàs1Institut de Matemàtiques i Aplicacions de Castelló (IMAC) and Departament de Matemàtiques, Universitat Jaume I, 12071-Castellón, SpainInstitut de Matemàtiques i Aplicacions de Castelló (IMAC) and Departament de Matemàtiques, Universitat Jaume I, 12071-Castellón, SpainNew families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a way that each part is explicitly solvable. The methods are obtained by applying different optimization criteria and preserve geometric properties of the continuous problem by construction. Different numerical examples exhibit their improved performance with respect to previous splitting methods in the literature.https://www.mdpi.com/2227-7390/8/4/533composition methodssplitting methodssystems separable into three partsgeometric numerical integrators
collection DOAJ
language English
format Article
sources DOAJ
author Fernando Casas
Alejandro Escorihuela-Tomàs
spellingShingle Fernando Casas
Alejandro Escorihuela-Tomàs
Composition Methods for Dynamical Systems Separable into Three Parts
Mathematics
composition methods
splitting methods
systems separable into three parts
geometric numerical integrators
author_facet Fernando Casas
Alejandro Escorihuela-Tomàs
author_sort Fernando Casas
title Composition Methods for Dynamical Systems Separable into Three Parts
title_short Composition Methods for Dynamical Systems Separable into Three Parts
title_full Composition Methods for Dynamical Systems Separable into Three Parts
title_fullStr Composition Methods for Dynamical Systems Separable into Three Parts
title_full_unstemmed Composition Methods for Dynamical Systems Separable into Three Parts
title_sort composition methods for dynamical systems separable into three parts
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2020-04-01
description New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a way that each part is explicitly solvable. The methods are obtained by applying different optimization criteria and preserve geometric properties of the continuous problem by construction. Different numerical examples exhibit their improved performance with respect to previous splitting methods in the literature.
topic composition methods
splitting methods
systems separable into three parts
geometric numerical integrators
url https://www.mdpi.com/2227-7390/8/4/533
work_keys_str_mv AT fernandocasas compositionmethodsfordynamicalsystemsseparableintothreeparts
AT alejandroescorihuelatomas compositionmethodsfordynamicalsystemsseparableintothreeparts
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