分数阶扩散方程中多参数联合数值反演

Numerical Inversions of Joint Parameters in Fractional Diffusion Equation

考虑一维空间分数阶扩散方程中同时确定空间微分阶数、扩散系数和源项的多参数联合反演问题.基于空间分数阶导数离散系数的性质和快速傅里叶变换,给出求解正问题的一种新的差分格式.利用同伦正则化方法对所提的空间微分阶数、扩散系数和源项的多参数联合反演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:同伦正则化算法对空间分数阶扩散中的多参数联合反演是有效的.

A joint parameters inversion problem of determining the space fractional diffusion order,diffusion coefficient and source term simultaneously in 1-dimentional space fractional diffusion equation is studied.Using the property of the discrete coefficient of fractional derivative and the fast Fourier transformation,a new finite difference scheme for solving the forward problem is given.Numerical inversions with accurate data and noisy data for the joint parameters inversion problem using homotopy regularization algorithm is discussed.The numerical results show that the homotopy regularization algorithm is efficient for the joint parameters inversion in the space fractional diffusion.