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A second-order accurate numerical method for a fractional wave equation

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Abstract

We study a generalized Crank–Nicolson scheme for the time discretization of a fractional wave equation, in combination with a space discretization by linear finite elements. The scheme uses a non-uniform grid in time to compensate for the singular behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assuming that the spatial domain is convex or smooth, we show that the error is of order k 2 + h 2, where k and h are the parameters for the time and space meshes, respectively.

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Authors and Affiliations

  1. School of Mathematics and Statistics, The University of New South Wales, Sydney, 2052, Australia

    William McLean

  2. Department of Mathematical Sciences, KFUPM, Dhahran, 31261, Saudi Arabia

    Kassem Mustapha

Authors
  1. William McLean
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  2. Kassem Mustapha
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Correspondence to William McLean.

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McLean, W., Mustapha, K. A second-order accurate numerical method for a fractional wave equation. Numer. Math. 105, 481–510 (2007). https://doi.org/10.1007/s00211-006-0045-y

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  • DOI: https://doi.org/10.1007/s00211-006-0045-y

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