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Convolution quadrature time discretization of fractional diffusion-wave equations

Authors: Eduardo Cuesta, Christian Lubich and Cesar Palencia
Journal: Math. Comp. 75 (2006), 673-696
MSC (2000): Primary 65R20, 65M15; Secondary 26A33, 45K05
Published electronically: January 23, 2006
MathSciNet review: 2196986
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Abstract: We propose and study a numerical method for time discretization of linear and semilinear integro-partial differential equations that are intermediate between diffusion and wave equations, or are subdiffusive. The method uses convolution quadrature based on the second-order backward differentiation formula. Second-order error bounds of the time discretization and regularity estimates for the solution are shown in a unified way under weak assumptions on the data in a Banach space framework. Numerical experiments illustrate the theoretical results.

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Additional Information

Eduardo Cuesta
Affiliation: Departamento de Matemática Aplicada, Escuela Politécnica, Universidad de Valladolid, Francisco de Mendizábal 1, 47014, Valladolid, Spain

Christian Lubich
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany

Cesar Palencia
Affiliation: Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid, Prado de la Magdalena s/n, 47005, Valladolid, Spain

Keywords: Anomalous diffusion, parabolic equation with memory, time discretization, convolution quadrature, fractional BDF method, error analysis, regularity
Received by editor(s): January 20, 2004
Received by editor(s) in revised form: September 29, 2004
Published electronically: January 23, 2006
Additional Notes: The first and third authors were supported by Grant MCYT BFM2001-2013 cofinanced by FEDER funds. The second author was supported by DFG SFB 382
Article copyright: © Copyright 2006 American Mathematical Society

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