Numerische Mathematik

, Volume 105, Issue 3, pp 481-510

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

  • William McLeanAffiliated withSchool of Mathematics and Statistics, The University of New South Wales Email author 
  • , Kassem MustaphaAffiliated withDepartment of Mathematical Sciences, KFUPM

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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.

Mathematics Subject Classification (2000)

26A33 45J05 65M12 65M15 65M60