Blanes Zamora, S.; Casas, F.; Murua, A. (2024). Splitting methods for differential equations. ACTA NUMERICA. 33:1-161. https://doi.org/10.1017/S0962492923000077
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/211445
Title:
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Splitting methods for differential equations
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Author:
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Blanes Zamora, Sergio
Casas, Fernando
Murua, Ander
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Issued date:
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Abstract:
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[EN] This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely ...[+]
[EN] This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class of integrators are composition methods, in which one or several low-order schemes are composed to construct higher-order numerical approximations to the exact solution. We analyse in detail the order conditions that have to be satisfied by these classes of methods to achieve a given order, and provide some insight about their qualitative properties in connection with geometric numerical integration and the treatment of highly oscillatory problems. Since splitting methods have received considerable attention in the realm of partial differential equations, we also cover this subject in the present survey, with special attention to parabolic equations and their problems. An exhaustive list of methods of different orders is collected and tested on simple examples. Finally, some applications of splitting methods in different areas, ranging from celestial mechanics to statistics, are also provided.
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Subjects:
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Differential equations
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Splitting methods
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Composition methods
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Copyrigths:
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Reconocimiento (by)
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Source:
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ACTA NUMERICA. (issn:
0962-4929
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DOI:
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10.1017/S0962492923000077
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Publisher:
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Cambridge University Press
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Publisher version:
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https://doi.org/10.1017/S0962492923000077
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Project ID:
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info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136585NB-C21/ES/NUEVAS APLICACIONES DE METODOS DE INTEGRACION NUMERICA GEOMETRICA A PROBLEMAS EVOLUTIVOS, ECUACIONES DIFERENCIALES ESTOCASTICAS Y SIMULACIONES MONTECARLO/
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136585NB-C22/ES/NUEVAS APLICACIONES DE LOS INTEGRADORES NUMERICOS GEOMETRICOS A PROBLEMAS DE EVOLUCION, ECUACIONES DIFERENCIALES ESTOCASTICAS Y SIMULACIONES MONTE CARLO HAMILTONIANAS/
info:eu-repo/grantAgreement/GVA//CIAICO%2F2021%2F180/
info:eu-repo/grantAgreement/Eusko Jaurlaritza//ITI456-22/
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Thanks:
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This work has been funded by Ministerio de Ciencia e Innovacion (Spain) through projects PID2022-136585NB-C21 and PID2022-136585NB-C22, MCIN/AEI/10.13039/501100011033/FEDER, UE, and also by Generalitat Valenciana (Spain) ...[+]
This work has been funded by Ministerio de Ciencia e Innovacion (Spain) through projects PID2022-136585NB-C21 and PID2022-136585NB-C22, MCIN/AEI/10.13039/501100011033/FEDER, UE, and also by Generalitat Valenciana (Spain) through project CIAICO/2021/180. AM has also received funding from the Department of Education of the Basque Government through the Consolidated Research Group MATHMODE (ITI456-22).
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Type:
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Artículo
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