An ADI Crank–Nicolson Orthogonal Spline Collocation Method for the Two-Dimensional Fractional Diffusion-Wave Equation
An ADI Crank–Nicolson Orthogonal Spline Collocation Method for the Two-Dimensional Fractional Diffusion-Wave Equation
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DOI：
10.1007/s10915-015-0003-x
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发表时间：
2014-05
影响因子：
2.5
通讯作者：
G. Fairweather;Xuehua Yang;Da Xu;Haixiang Zhang
中科院分区：
文献类型：
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作者：
G. Fairweather;Xuehua Yang;Da Xu;Haixiang Zhang
本文提出并分析了一种求解二维时间分数阶扩散波方程的新方法。在该方法中，正交样条配置用于空间离散和，对于时间步进，一种新的交替方向隐式方法的基础上的Crank-Nicolson方法结合的时间Caputo阶导数的近似。证明了该格式是稳定的，在各种范数下具有最优精度。数值实验证明了预测的全局收敛速度和超收敛性。
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 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.