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, Juan Pablo, Rial, Diego Fernando
Publicado: 2014
Materias:
Lie-Trotter
Semilinear problems
Splitting integrators
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15396746_v13_n1_p83_Borgna
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 paper:paper_15396746_v13_n1_p83_Borgna
record_format dspace
spelling paper:paper_15396746_v13_n1_p83_Borgna2023-06-08T16:21:04Z General splitting methods for abstract semilinear evolution equations Borgna, Juan Pablo Rial, Diego Fernando 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. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15396746_v13_n1_p83_Borgna 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, Juan Pablo
Rial, Diego Fernando
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.
author Borgna, Juan Pablo
Rial, Diego Fernando
author_facet Borgna, Juan Pablo
Rial, Diego Fernando
author_sort Borgna, Juan Pablo
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
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15396746_v13_n1_p83_Borgna
http://hdl.handle.net/20.500.12110/paper_15396746_v13_n1_p83_Borgna
work_keys_str_mv AT borgnajuanpablo generalsplittingmethodsforabstractsemilinearevolutionequations
AT rialdiegofernando generalsplittingmethodsforabstractsemilinearevolutionequations
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