A second-order accurate numerical method for a fractional wave equation
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- McLean, W. & Mustapha, K. Numer. Math. (2007) 105: 481. doi:10.1007/s00211-006-0045-y
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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 k2 + h2, where k and h are the parameters for the time and space meshes, respectively.