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

作者：McLean William^*; Mustapha Kassem

来源：Numerische Mathematik, 2007, 105(3): 481-510.

DOI：10.1007/s00211-006-0045-y

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.

• 出版日期2007-1
• 单位中国石油大学（北京）