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Extrapolating for attaining high precision solutions for fractional partial differential equations

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Abstract

This paper aims at obtaining a high precision numerical approximation for fractional partial differential equations. This is achieved through appropriate discretizations: firstly we consider the application of shifted Legendre or Chebyshev polynomials to get a spatial discretization, followed by a temporal discretization where we use the Implicit Euler method (although any other temporal integrator could be used). Finally, the use of an extrapolation technique is considered for improving the numerical results. In this way a very accurate solution is obtained. An algorithm is presented, and numerical results are shown to demonstrate the validity of the present technique.

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Authors and Affiliations

  1. CMUC, Departamento de Matematica, University of Coimbra, Coimbra, Portugal

    Fernanda Simões Patrício

  2. Laboratory of Biostatistics and Medical Informatics and IBILI Faculty of Medicine, University of Coimbra, Coimbra, Portugal

    Miguel Patrício

  3. Escuela Politécnica Superior de Zamora, University of Salamanca, Zamora, Spain

    Higinio Ramos

Authors
  1. Fernanda Simões Patrício
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  2. Miguel Patrício
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  3. Higinio Ramos
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Correspondence to Fernanda Simões Patrício.

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Patrício, F.S., Patrício, M. & Ramos, H. Extrapolating for attaining high precision solutions for fractional partial differential equations. FCAA 21, 1506–1523 (2018). https://doi.org/10.1515/fca-2018-0079

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  • DOI: https://doi.org/10.1515/fca-2018-0079

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