Convolution quadrature time discretization of fractional diffusion-wave equations
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- by Eduardo Cuesta, Christian Lubich and Cesar Palencia PDF
- Math. Comp. 75 (2006), 673-696 Request permission
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.References
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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
- Email: eduardo@mat.uva.es
- Christian Lubich
- Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
- MR Author ID: 116445
- Email: lubich@na.uni-tuebingen.de
- Cesar Palencia
- Affiliation: Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid, Prado de la Magdalena s/n, 47005, Valladolid, Spain
- Email: palencia@mac.cie.uva.es
- 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
- © Copyright 2006 American Mathematical Society
- Journal: Math. Comp. 75 (2006), 673-696
- MSC (2000): Primary 65R20, 65M15; Secondary 26A33, 45K05
- DOI: https://doi.org/10.1090/S0025-5718-06-01788-1
- MathSciNet review: 2196986