Numerische Mathematik

, Volume 105, Issue 3, pp 481–510

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

Article

DOI: 10.1007/s00211-006-0045-y

Cite this article as:
McLean, W. & Mustapha, K. Numer. Math. (2007) 105: 481. doi:10.1007/s00211-006-0045-y

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 k2 + h2, where k and h are the parameters for the time and space meshes, respectively.

Mathematics Subject Classification (2000)

26A33 45J05 65M12 65M15 65M60 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsThe University of New South WalesSydneyAustralia
  2. 2.Department of Mathematical SciencesKFUPMDhahranSaudi Arabia

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