Artículo
General splitting methods for abstract semilinear evolution equations
Borgna, Juan Pablo
; de Leo, Mariano Fernando
; Rial, Diego Fernando
; Sanchez Fernandez de la Vega, Constanza Mariel
Fecha de publicación:
01/2015
Editorial:
International Press Boston
Revista:
Communications in Mathematical Sciences
ISSN:
1539-6746
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
In this paper we present a unified picture concerning general splitting methods for solving a large class of semilinear problems: nonlinear Schr¨odinger, Schr¨odinger–Poisson, Gross– Pitaevskii equations, etc. This picture includes as particular instances known schemes such as LieTrotter, 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.
Palabras clave:
Lie-Trotter
,
Splitting Integrators
,
Semilinear Problems
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Borgna, Juan Pablo; de Leo, Mariano Fernando; Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; General splitting methods for abstract semilinear evolution equations; International Press Boston; Communications in Mathematical Sciences; 13; 1; 1-2015; 83-101
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