An ADI Crank-Nicolson Orthogonal Spline Collocation Method for the Two-Dimensional Fractional Diffusion-Wave Equation
Numerical Analysis
2014-05-14 v1
Abstract
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 -approximation of the time Caputo derivative of order . 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.
Cite
@article{arxiv.1405.3264,
title = {An ADI Crank-Nicolson Orthogonal Spline Collocation Method for the Two-Dimensional Fractional Diffusion-Wave Equation},
author = {Graeme Fairweather and Xuehua Yang and Da Xu and Haixiang Zhang},
journal= {arXiv preprint arXiv:1405.3264},
year = {2014}
}