A modified fractional Landweber method for a backward problem for the inhomogeneous time-fractional diffusion equation in a cylinder. Issue 11 (1st November 2020) - Yang, Shuping; Xiong, Xiangtuan; Han, Yaozong
Abstract : In this paper, we consider a backward problem for the inhomogeneous time-fractional diffusion equation in a cylinder. Such a problem is ill-posed. Based on the solution given by the separation of variables, we apply a modified fractional Landweber method to solve it. Error estimates are presented under the a-priori and the a-posteriori choice rules for regularization parameters, respectively. Relative to the classical Landweber method, the modified fractional Landweber method can reduce the total number of iterations to achieve the same accuracy. Numerical example is given to show the validity of the scheme.