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Abstract:

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.

Registro:

Documento: Artículo
Título:High-order time-splitting methods for irreversible equations
Autor:De Leo, M.; Rial, D.; De La Vega, C.S.
Filiación:Instituto de Ciencias, Universidad de General Sarmiento, Juan María Gutiérrez 1150, Los Polvorines, Pcia de Buenos Aires, C1613EGA, Argentina
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Intendente Guiraldes 2160, Ciudad Universitaria, Pabellon, Buenos Aires, C1428EGA, Argentina
Instituto de Matemática Luis Santaló, IMAS-CONICET, Buenos Aires, Argentina
Palabras clave:high-order method; irreversible dynamics; splitting methods
Año:2016
Volumen:36
Número:4
Página de inicio:1842
Página de fin:1866
DOI: http://dx.doi.org/10.1093/imanum/drv058
Título revista:IMA Journal of Numerical Analysis
Título revista abreviado:IMA J. Numer. Anal.
ISSN:02724979
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v36_n4_p1842_DeLeo

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Citas:

---------- APA ----------
De Leo, M., Rial, D. & De La Vega, C.S. (2016) . High-order time-splitting methods for irreversible equations. IMA Journal of Numerical Analysis, 36(4), 1842-1866.
http://dx.doi.org/10.1093/imanum/drv058
---------- CHICAGO ----------
De Leo, M., Rial, D., De La Vega, C.S. "High-order time-splitting methods for irreversible equations" . IMA Journal of Numerical Analysis 36, no. 4 (2016) : 1842-1866.
http://dx.doi.org/10.1093/imanum/drv058
---------- MLA ----------
De Leo, M., Rial, D., De La Vega, C.S. "High-order time-splitting methods for irreversible equations" . IMA Journal of Numerical Analysis, vol. 36, no. 4, 2016, pp. 1842-1866.
http://dx.doi.org/10.1093/imanum/drv058
---------- VANCOUVER ----------
De Leo, M., Rial, D., De La Vega, C.S. High-order time-splitting methods for irreversible equations. IMA J. Numer. Anal. 2016;36(4):1842-1866.
http://dx.doi.org/10.1093/imanum/drv058