变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 Time-Fractional Diffusion Equation
DOI: 10.12677/AAM.2015.44041, PDF, HTML, XML,  被引量 下载: 2,988  浏览: 7,860  国家自然科学基金支持
作者: 刘迪, 孙春龙, 李功胜*, 贾现正：山东理工大学理学院，山东 淄博
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: 对于变分数阶扩散方程，给出一个隐式差分求解格式。进一步讨论由内点观测数据确定微分阶数的一个反问题，应用同伦正则化算法在不同参数取值条件下进行数值反演模拟。数值结果表明当微分阶数接近于1时，数值求解及其参数反演效果较好。
Abstract: An implicit finite difference scheme is introduced to solve the variable-order time-fractional diffu-sion equation, and an inverse problem of determining the variable fractional order is set forth using the additional measurements at one interior point. The homotopy regularization algorithm is applied to solve the inverse problem, and numerical examples are presented. The computational and inversion results demonstrate that the variable order has important influence on the problem, and that the computations become effective when the variable order goes to 1.
文章引用：刘迪, 孙春龙, 李功胜, 贾现正. 变分数阶扩散方程微分阶数的数值反演[J]. 应用数学进展, 2015, 4(4): 326-335. http://dx.doi.org/10.12677/AAM.2015.44041

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