2014/05/13 by Fairweather, Graeme, Yang, Xuehua, Xu, Da +1
#35R11 #65M12 #65M15 #65M70 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1405.3264
A new method is formulated and analyzed for the approximate solution of a two-dimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the time-stepping, a novel alternating direction implicit (ADI) method based on the Crank-Nicolson method combined with the L1-approximation of the time Caputo derivative of order α∈(1,2). It is proved that this scheme is stable, and of optimal accuracy in various norms. Numerical experiments demonstrate the predicted global convergence rates and also superconvergence.