Mostrar el registro sencillo del ítem
dc.contributor.author
Acosta, Gabriel
dc.contributor.author
Borthagaray, Juan Pablo
dc.contributor.author
Bruno, Oscar Ricardo
![Se ha confirmado la validez de este valor de autoridad por un usuario](/themes/CONICETDigital/images/authority_control/invisible.gif)
dc.contributor.author
Maas, Martín Daniel
![Se ha confirmado la validez de este valor de autoridad por un usuario](/themes/CONICETDigital/images/authority_control/invisible.gif)
dc.date.available
2017-09-04T19:47:28Z
dc.date.issued
2017-03
dc.identifier.citation
Acosta, Gabriel; Borthagaray, Juan Pablo; Bruno, Oscar Ricardo; Maas, Martín Daniel; Regularity theory and high order numerical methods for the (1D)-fractional Laplacian; American Mathematical Society; Mathematics Of Computation; 3-2017; 1-37
dc.identifier.issn
0025-5718
dc.identifier.uri
http://hdl.handle.net/11336/23611
dc.description.abstract
This paper presents regularity results and associated high-order numerical methods for one-dimensional Fractional-Laplacian boundary-value problems. On the basis of a factorization of solutions as a product of a certain edge-singular weight $w$ times a ``regular´´ unknown, a characterization of the regularity of solutions is obtained in terms of the smoothness of the corresponding right-hand sides. In particular, for right-hand sides which are analytic in a Bernstein Ellipse, analyticity in the same Bernstein Ellipse is obtained for the ``regular´´ unknown. Moreover, a sharp Sobolev regularity result is presented which completely characterizes the co-domain of the Fractional-Laplacian operator in terms of certain weighted Sobolev spaces introduced in (Babu{s}ka and Guo, SIAM J. Numer. Anal. 2002). The present theoretical treatment relies on a full eigendecomposition for a certain weighted integral operator in terms of the Gegenbauer polynomial basis. The proposed Gegenbauer-based Nystr"om numerical method for the Fractional-Laplacian Dirichlet problem, further, is significantly more accurate and efficient than other algorithms considered previously. The sharp error estimates presented in this paper indicate that the proposed algorithm is spectrally accurate, with convergence rates that only depend on the smoothness of the right-hand side. In particular, convergence is exponentially fast (resp. faster than any power of the mesh-size) for analytic (resp. infinitely smooth) right-hand sides. The properties of the algorithm are illustrated with a variety of numerical results.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
American Mathematical Society
![Se ha confirmado la validez de este valor de autoridad por un usuario](/themes/CONICETDigital/images/authority_control/invisible.gif)
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
High Order Numerical Methods
dc.subject
Gegenbauer Polynomials
dc.subject
Hypersingular Integral Equations
dc.subject
Fractional Laplacian
dc.subject.classification
Otras Matemáticas
![Se ha confirmado la validez de este valor de autoridad por un usuario](/themes/CONICETDigital/images/authority_control/invisible.gif)
dc.subject.classification
Matemáticas
![Se ha confirmado la validez de este valor de autoridad por un usuario](/themes/CONICETDigital/images/authority_control/invisible.gif)
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
![Se ha confirmado la validez de este valor de autoridad por un usuario](/themes/CONICETDigital/images/authority_control/invisible.gif)
dc.title
Regularity theory and high order numerical methods for the (1D)-fractional Laplacian
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-08-25T19:55:20Z
dc.journal.pagination
1-37
dc.journal.pais
Estados Unidos
![Se ha confirmado la validez de este valor de autoridad por un usuario](/themes/CONICETDigital/images/authority_control/invisible.gif)
dc.journal.ciudad
Nueva York
dc.description.fil
Fil: Acosta, Gabriel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
dc.description.fil
Fil: Borthagaray, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
dc.description.fil
Fil: Bruno, Oscar Ricardo. California Institute Of Technology; Estados Unidos
dc.description.fil
Fil: Maas, Martín Daniel. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina
dc.journal.title
Mathematics Of Computation
![Se ha confirmado la validez de este valor de autoridad por un usuario](/themes/CONICETDigital/images/authority_control/invisible.gif)
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/mcom/earlyview/#mcom3276
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1090/mcom/3276
Archivos asociados