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Numerical Algorithms

, Volume 74, Issue 4, pp 1061–1082 | Cite as

Solving mixed classical and fractional partial differential equations using short–memory principle and approximate inverses

  • Daniele BertacciniEmail author
  • Fabio Durastante
Original Paper

Abstract

The efficient numerical solution of the large linear systems of fractional differential equations is considered here. The key tool used is the short–memory principle. The latter ensures the decay of the entries of the inverse of the discretized operator, whose inverses are approximated here by a sequence of sparse matrices. On this ground, we propose to solve the underlying linear systems by these approximations or by iterative solvers using sequence of preconditioners based on the above mentioned inverses.

Keywords

Preconditioners Fractional calculus Iterative methods 

Mathematics Subject Classification (2010)

65F10 65F08 26A33 65Y10 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Dipartimento di Scienza e Alta TecnologiaUniversità dell’InsubriaComoItaly

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