Novel parallel in time integrators for ODEs

Autor:	Sergio Blanes
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	Generalization Differential equation Applied Mathematics Computation Extrapolation Parallel in time methods Symmetric second order methods Set (abstract data type) Numerical methods for ODEs Integrator Lie algebra Composition methods Applied mathematics Linear combination Mathematics
Zdroj:	RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname
ISSN:	2019-1049
Popis:	[EN] We present a novel class of integrators for differential equations that are suitable for parallel in time computation, whose structure can be considered as a generalization of the extrapolation methods. Starting with a low order integrator (preferably a symmetric second order one) we can build a set of second order schemes by few compositions of this basic scheme that can be computed in parallel. Then, a proper linear combination of the results (obtained from the order conditions associated to the corresponding Lie algebra) allows us to obtain new higher order methods. In this letter we present the structure of the methods, how to obtain several methods, we notice some order barriers that depend on the structure of the compositions used and finally, we show how this analysis can be further carried to obtain new and higher order schemes. This work was supported by Ministerio de Ciencia e Innovacion (Spain) through project PID2019-104927GB-C21/AEI/10.13039/501100011033.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ab6bb3c68f21c8eb3c392437652009ba http://hdl.handle.net/10251/181546 Zobrazit plný text záznamu