Artículo
Borgna, J.P.; de Leo, M.; Rial, D.; de La Vega, C.S. "General splitting methods for abstract semilinear evolution equations" (2014) Communications in Mathematical Sciences. 13(1):83-101
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Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | General splitting methods for abstract semilinear evolution equations |
| Autor: | Borgna, J.P.; de Leo, M.; Rial, D.; de La Vega, C.S. |
| Filiación: | Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, Los Polvorines, Buenos Aires, 1613, Argentina IMAS - CONICET and Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150 (1613), Los Polvorines, Buenos Aires, Argentina |
| Palabras clave: | Lie-Trotter; Semilinear problems; Splitting integrators |
| Año: | 2014 |
| Volumen: | 13 |
| Número: | 1 |
| Página de inicio: | 83 |
| Página de fin: | 101 |
| Título revista: | Communications in Mathematical Sciences |
| Título revista abreviado: | Commun. Math. Sci. |
| ISSN: | 15396746 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15396746_v13_n1_p83_Borgna |
Referencias:
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Citas:
---------- APA ----------
Borgna, J.P., de Leo, M., Rial, D. & de La Vega, C.S. (2014) . General splitting methods for abstract semilinear evolution equations. Communications in Mathematical Sciences, 13(1), 83-101.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15396746_v13_n1_p83_Borgna [ ]
---------- CHICAGO ----------
Borgna, J.P., de Leo, M., Rial, D., de La Vega, C.S. "General splitting methods for abstract semilinear evolution equations" . Communications in Mathematical Sciences 13, no. 1 (2014) : 83-101.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15396746_v13_n1_p83_Borgna [ ]
---------- MLA ----------
Borgna, J.P., de Leo, M., Rial, D., de La Vega, C.S. "General splitting methods for abstract semilinear evolution equations" . Communications in Mathematical Sciences, vol. 13, no. 1, 2014, pp. 83-101.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15396746_v13_n1_p83_Borgna [ ]
---------- VANCOUVER ----------
Borgna, J.P., de Leo, M., Rial, D., de La Vega, C.S. General splitting methods for abstract semilinear evolution equations. Commun. Math. Sci. 2014;13(1):83-101.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15396746_v13_n1_p83_Borgna [ ]
