变空间分数阶扩散方程微分阶数的数值反演
Numerical Inversion for the Fractional Order in the Variable-Order Space-Fractional Diffusion Equation
DOI: 10.12677/AAM.2017.64069, PDF, HTML, XML,  被引量 下载: 1,764  浏览: 3,921  科研立项经费支持
作者: 刘迪, 王淑香：广州航海学院基础教学部，广东 广州
关键词: 变分数阶扩散方程；反问题；同伦正则化；数值反演；Variable-Order Fractional Diffusion Equation； Inverse Problem； Homotopy Regularization Algorithm； Numerical Inversion
摘要: 本文探讨一维变空间分数阶对流扩散方程，应用改进了的Grunwald-Letnikov分数阶导数定义对方程进行了离散，建立了隐式差分格式，并证明了该差分法的收敛性和稳定性。其次应用同伦正则化算法给出一维变空间分数阶扩散模型微分阶数的数值反演模拟，并讨论不同条件下的反演结果。
Abstract: We consider a variable-order fractional advection-diffusion equation. Explicit approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, the homotopy regularization algorithm is applied to solve the inverse problem, and numerical examples are presented. 
文章引用：刘迪, 王淑香. 变空间分数阶扩散方程微分阶数的数值反演[J]. 应用数学进展, 2017, 6(4): 589-598. https://doi.org/10.12677/AAM.2017.64069

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