General splitting methods for abstract semilinear evolution equations

In this paper we present a unified picture concerning general splitting methods for solving a large class of semilinear problems: nonlinear Schrödinger, Schrödinger-Poisson, Gross- Pitaevskii equations, etc. This picture includes as particular instances known schemes such as Lie- Trotter, Strang, an...

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Autores principales:	Borgna, J.P., de Leo, M., Rial, D., de La Vega, C.S.
Formato:	JOUR
Materias:	Lie-Trotter Semilinear problems Splitting integrators
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_15396746_v13_n1_p83_Borgna
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_15396746_v13_n1_p83_Borgna
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spelling	todo:paper_15396746_v13_n1_p83_Borgna2023-10-03T16:22:53Z General splitting methods for abstract semilinear evolution equations Borgna, J.P. de Leo, M. Rial, D. de La Vega, C.S. Lie-Trotter Semilinear problems Splitting integrators In this paper we present a unified picture concerning general splitting methods for solving a large class of semilinear problems: nonlinear Schrödinger, Schrödinger-Poisson, Gross- Pitaevskii equations, etc. This picture includes as particular instances known schemes such as Lie- Trotter, Strang, and Ruth-Yoshida. The convergence result is presented in suitable Hilbert spaces related to the time regularity of the solution and is based on Lipschitz estimates for the nonlinearity. In addition, with extra requirements both on the regularity of the initial datum and on the nonlinearity, we show the linear convergence of these methods. We finally mention that in some special cases in which the linear convergence result is known, the assumptions we made are less restrictive. © 2015 International Press. Fil:Borgna, J.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 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_15396746_v13_n1_p83_Borgna
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Lie-Trotter Semilinear problems Splitting integrators
spellingShingle	Lie-Trotter Semilinear problems Splitting integrators Borgna, J.P. de Leo, M. Rial, D. de La Vega, C.S. General splitting methods for abstract semilinear evolution equations
topic_facet	Lie-Trotter Semilinear problems Splitting integrators
description	In this paper we present a unified picture concerning general splitting methods for solving a large class of semilinear problems: nonlinear Schrödinger, Schrödinger-Poisson, Gross- Pitaevskii equations, etc. This picture includes as particular instances known schemes such as Lie- Trotter, Strang, and Ruth-Yoshida. The convergence result is presented in suitable Hilbert spaces related to the time regularity of the solution and is based on Lipschitz estimates for the nonlinearity. In addition, with extra requirements both on the regularity of the initial datum and on the nonlinearity, we show the linear convergence of these methods. We finally mention that in some special cases in which the linear convergence result is known, the assumptions we made are less restrictive. © 2015 International Press.
format	JOUR
author	Borgna, J.P. de Leo, M. Rial, D. de La Vega, C.S.
author_facet	Borgna, J.P. de Leo, M. Rial, D. de La Vega, C.S.
author_sort	Borgna, J.P.
title	General splitting methods for abstract semilinear evolution equations
title_short	General splitting methods for abstract semilinear evolution equations
title_full	General splitting methods for abstract semilinear evolution equations
title_fullStr	General splitting methods for abstract semilinear evolution equations
title_full_unstemmed	General splitting methods for abstract semilinear evolution equations
title_sort	general splitting methods for abstract semilinear evolution equations
url	http://hdl.handle.net/20.500.12110/paper_15396746_v13_n1_p83_Borgna
work_keys_str_mv	AT borgnajp generalsplittingmethodsforabstractsemilinearevolutionequations AT deleom generalsplittingmethodsforabstractsemilinearevolutionequations AT riald generalsplittingmethodsforabstractsemilinearevolutionequations AT delavegacs generalsplittingmethodsforabstractsemilinearevolutionequations
_version_	1807322540939411456

General splitting methods for abstract semilinear evolution equations

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