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

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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.

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  1. Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Lecce, Italy

    M. Popolizio

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  1. M. Popolizio
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Popolizio, M. A matrix approach for partial differential equations with Riesz space fractional derivatives. Eur. Phys. J. Spec. Top. 222, 1975–1985 (2013). https://doi.org/10.1140/epjst/e2013-01978-8

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  • DOI: https://doi.org/10.1140/epjst/e2013-01978-8

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