A Compact ADI Scheme for Two-dimensional Caputo-Hadamard Fractional Sub-diffusion Equations
关凯菁 1莫艳 1汪志波1
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作者信息
1. 广东工业大学 数学与统计学院,广东 广州 510520
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摘要
本文讨论了二维时间分数阶Caputo-Hadamard慢扩散方程的交替方向隐式(Alternating Direction Implicit,ADI)紧致差分格式.首先,在指数型网格上对Caputo-Hadamard型分数阶导数进行离散;其次,利用紧致ADI方法将高维问题转化为2个一维问题;根据离散系数的性质,利用数学归纳法证明了差分格式的稳定性和收敛性;最后,对具体模型进行数值求解.算例验证了上述理论分析的有效性.
Abstract
The compact alternating direction implicit(ADI)scheme for two-dimensional Caputo-Hadamard fractional sub-differential equations is studied.Firstly,the Caputo-Hadamard fractional derivative on exponential type meshes is approximated.Secondly,in order to solve the high-dimensional problems,a compact ADI method is proposed.With the help of mathematical induction and the properties of discrete coefficients,the stability and convergence of the proposed scheme are analyzed.Ultimately,an example is presented to show the effective of our analysis.
关键词
Caputo-Hadamard慢扩散方程/指数型网格/紧致交替隐式方法/稳定性和收敛性
Key words
Caputo-Hadamard fractional differential equations/exponential type meshes/compact alternating direction implicit method/stability and convergence
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