AAM  >> Vol. 4 No. 4 (November 2015)

    Numerical Inversion for the Fractional Order in the Variable-Order Time-Fractional Diffusion Equation

  • 全文下载: PDF(587KB) HTML   XML   PP.326-335   DOI: 10.12677/AAM.2015.44041  
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刘迪,孙春龙,李功胜,贾现正:山东理工大学理学院,山东 淄博

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


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.

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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