A Compact Difference Scheme for Fractional Sub-diffusion Equations with the Spatially Variable Coefficient Under Neumann Boundary Conditions
A Compact Difference Scheme for Fractional Sub-diffusion Equations with the Spatially Variable Coefficient Under Neumann Boundary Conditions
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DOI：
10.1007/s10915-015-0040-5
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发表时间：
2016-02
影响因子：
2.5
通讯作者：
Seakweng Vong;Pin Lyu;Zhibo Wang
中科院分区：
文献类型：
--
作者：
Seakweng Vong;Pin Lyu;Zhibo Wang
本文对Neumann边界条件下具有空间变系数的分数阶次扩散方程，导出了一种具有全局收敛阶的紧致差分格式。通过对系数矩阵的微妙分解，克服了变系数和Neumann边界条件带来的困难。利用其矩阵形式，用能量法研究了该格式的稳定性和收敛性。理论结果得到了数值实验的支持。
In this paper, a compact finite difference scheme with global convergence orderis derived for fractional sub-diffusion equations with the spatially variable coefficient subject to Neumann boundary conditions. The difficulty caused by the variable coefficient and the Neumann boundary conditions is overcome by subtle decomposition of the coefficient matrices. The stability and convergence of the proposed scheme are studied using its matrix form by the energy method. The theoretical results are supported by numerical experiments.