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The European Physical Journal Special Topics

, Volume 222, Issue 8, pp 1975–1985 | Cite as

A matrix approach for partial differential equations with Riesz space fractional derivatives

  • M. PopolizioEmail author
Regular Article

Abstract

Fractional partial differential equations are emerging in many scientific fields and their numerical solution is becoming a fundamental topic. In this paper we consider the Riesz fractional derivative operator and its discretization by fractional centered differences. The resulting matrix is studied, with an interesting result on a connection between the decay behavior of its entries and the short memory principle from fractional calculus. The Shift-and-Invert method is then applied to approximate the solution of the partial differential equation as the action of the matrix exponential on a suitable vector which mimics the given initial conditions. The numerical results confirm the good approximation quality and encourage the use of the proposed approach.

Keywords

European Physical Journal Special Topic Fractional Derivative Fractional Calculus Krylov Subspace Matrix Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Fisica “Ennio De Giorgi”Università del SalentoLecceItaly

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