High-order time-splitting methods for irreversible equations

In this work, high-order splitting methods of integration without negative steps are shown which can be used in irreversible problems, like reaction-diffusion or complex Ginzburg-Landau equations. These methods consist of suitable affine combinations of Lie-Tortter schemes with different positive st...

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Detalles Bibliográficos
Autores principales:	De Leo, M., Rial, D., De La Vega, C.S.
Formato:	JOUR
Materias:	high-order method irreversible dynamics splitting methods
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_02724979_v36_n4_p1842_DeLeo
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_02724979_v36_n4_p1842_DeLeo
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spelling	todo:paper_02724979_v36_n4_p1842_DeLeo2023-10-03T15:15:17Z High-order time-splitting methods for irreversible equations De Leo, M. Rial, D. De La Vega, C.S. high-order method irreversible dynamics splitting methods In this work, high-order splitting methods of integration without negative steps are shown which can be used in irreversible problems, like reaction-diffusion or complex Ginzburg-Landau equations. These methods consist of suitable affine combinations of Lie-Tortter schemes with different positive steps. The number of basic steps for these methods grows quadratically with the order, while for symplectic methods, the growth is exponential. Furthermore, the calculations can be performed in parallel, so that the computation time can be significantly reduced using multiple processors. Convergence results of these methods are proved for a large range of semilinear problems, which includes reaction-diffusion systems and dissipative perturbation of Hamiltonian systems. © 2015 The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. Fil:Rial, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02724979_v36_n4_p1842_DeLeo
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	high-order method irreversible dynamics splitting methods
spellingShingle	high-order method irreversible dynamics splitting methods De Leo, M. Rial, D. De La Vega, C.S. High-order time-splitting methods for irreversible equations
topic_facet	high-order method irreversible dynamics splitting methods
description	In this work, high-order splitting methods of integration without negative steps are shown which can be used in irreversible problems, like reaction-diffusion or complex Ginzburg-Landau equations. These methods consist of suitable affine combinations of Lie-Tortter schemes with different positive steps. The number of basic steps for these methods grows quadratically with the order, while for symplectic methods, the growth is exponential. Furthermore, the calculations can be performed in parallel, so that the computation time can be significantly reduced using multiple processors. Convergence results of these methods are proved for a large range of semilinear problems, which includes reaction-diffusion systems and dissipative perturbation of Hamiltonian systems. © 2015 The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
format	JOUR
author	De Leo, M. Rial, D. De La Vega, C.S.
author_facet	De Leo, M. Rial, D. De La Vega, C.S.
author_sort	De Leo, M.
title	High-order time-splitting methods for irreversible equations
title_short	High-order time-splitting methods for irreversible equations
title_full	High-order time-splitting methods for irreversible equations
title_fullStr	High-order time-splitting methods for irreversible equations
title_full_unstemmed	High-order time-splitting methods for irreversible equations
title_sort	high-order time-splitting methods for irreversible equations
url	http://hdl.handle.net/20.500.12110/paper_02724979_v36_n4_p1842_DeLeo
work_keys_str_mv	AT deleom highordertimesplittingmethodsforirreversibleequations AT riald highordertimesplittingmethodsforirreversibleequations AT delavegacs highordertimesplittingmethodsforirreversibleequations
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High-order time-splitting methods for irreversible equations

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