Effect of the nodes near boundary points on the stability analysis of sixth-order compact finite difference ADI scheme for the two-dimensional time fractional diffusion-wave equation

IF 0.3 Q4 MATHEMATICS Transactions of A Razmadze Mathematical Institute Pub Date : 2018-12-01 DOI:10.1016/j.trmi.2018.03.003

Z. Soori, A. Aminataei

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引用次数: 4

Abstract

In this paper, the aim is to present a high-order compact alternating direction implicit (ADI) scheme for the two-dimensional time fractional diffusion-wave (FDW) equation. The time fractional derivative which has been described in the Caputo’s sense is approximated by a scheme of order $O (τ^{3 - α})$ , $1 < α < 2$ and the space derivatives are discretized with a sixth-order compact procedure. The solvability, stability and $H^{1}$ norm of the scheme are proved. Numerical results are provided to verify the accuracy and efficiency of the proposed method of solution. The sixth-order accuracy in the space directions has not been achieved in previously studied schemes.

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边界点附近节点对二维时间分数阶扩散波动方程六阶紧致有限差分ADI格式稳定性分析的影响

本文的目的是给出二维时间分数扩散波方程的一种高阶紧致交替方向隐式格式。用一个O(τ3−α)， 1<α<2阶格式逼近了在Caputo意义上描述的时间分数阶导数，并用一个六阶紧化过程离散了空间导数。证明了该方案的可解性、稳定性和H1范数。数值结果验证了所提求解方法的准确性和有效性。在以往的研究方案中，空间方向的六阶精度尚未达到。

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