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计算数学  2014 

空间-时间分数阶变系数对流扩散方程微分阶数的数值反演

, PP. 113-132

Keywords: 空间-时间分数阶扩散,差分格式,稳定性与收敛性,微分阶数反问题,同伦正则化算法,数值反演

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Abstract:

考虑终值数据条件下一维空间-时间分数阶变系数对流扩散方程中同时确定空间微分阶数与时间微分阶数的反问题.基于对空间-时间分数阶导数的离散,给出求解正问题的一个隐式差分格式,通过对系数矩阵谱半径的估计,证明差分格式的无条件稳定性和收敛性.联合最佳摄动量算法和同伦方法引入同伦正则化算法,应用一种单调下降的Sigmoid型传输函数作为同伦参数,对所提微分阶数反问题进行精确数据与扰动数据情形下的数值反演.结果表明同伦正则化算法对于空间-时间分数阶反常扩散的参数反演问题是有效的.

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