This paper deals with some numerical issues about the rational approximation to fractional differential operators provided by the Padé approximants. In particular, the attention is focused on the fractional Laplacian and on the Caputo’s derivative which, in this context, occur into the definition of anomalous diffusion problems and of time fractional differential equations (FDEs), respectively. The paper provides the algorithms for an efficient implementation of the IMEX schemes for semi-discrete anomalous diffusion problems and of the short-memory-FBDF methods for Caputo’s FDEs.

Efficient implementation of rational approximations to fractional differential operators

Lidia Aceto
Primo
;
2018

Abstract

This paper deals with some numerical issues about the rational approximation to fractional differential operators provided by the Padé approximants. In particular, the attention is focused on the fractional Laplacian and on the Caputo’s derivative which, in this context, occur into the definition of anomalous diffusion problems and of time fractional differential equations (FDEs), respectively. The paper provides the algorithms for an efficient implementation of the IMEX schemes for semi-discrete anomalous diffusion problems and of the short-memory-FBDF methods for Caputo’s FDEs.
Aceto, Lidia; Novati, Paolo
File in questo prodotto:
File Dimensione Formato  
s10915-017-0633-2.pdf

solo utenti autorizzati

Descrizione: Articolo principale
Tipologia: Versione finale editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 990.75 kB
Formato Adobe PDF
990.75 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Revision2_JOMP-D-17-00186.pdf

embargo fino al 31/07/2019

Tipologia: Documento in Post-print
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 449.07 kB
Formato Adobe PDF
449.07 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/897184
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 10
social impact