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On the use of matrix functions for fractional partial differential equations

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  • Garrappa, Roberto
  • Popolizio, Marina

Abstract

The main focus of this paper is the solution of some partial differential equations of fractional order. Promising methods based on matrix functions are taken in consideration. The features of different approaches are discussed and compared with results provided by classical convolution quadrature rules. By means of numerical experiments accuracy and performance are examined.

Suggested Citation

  • Garrappa, Roberto & Popolizio, Marina, 2011. "On the use of matrix functions for fractional partial differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 1045-1056.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:5:p:1045-1056
    DOI: 10.1016/j.matcom.2010.10.009
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    References listed on IDEAS

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    1. Galeone, Luciano & Garrappa, Roberto, 2008. "Fractional Adams–Moulton methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1358-1367.
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    Cited by:

    1. Politi, Tiziano & Popolizio, Marina, 2015. "On stochasticity preserving methods for the computation of the matrix pth root," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 53-68.
    2. Marina Popolizio, 2019. "On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation," Mathematics, MDPI, vol. 7(12), pages 1-12, November.
    3. Abdelkawy, M.A. & Alyami, S.A., 2021. "Legendre-Chebyshev spectral collocation method for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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