Three Landweber iterative methods for solving the initial value problem of time-fractional diffusion-wave equation on spherically symmetric domain

In this paper, the inverse problem for identifying the initial value of time-fractional diffusion wave equation on spherically symmetric region is considered. The exact solution of this problem is obtained by using the method of separating variables and the property the Mittag-Leffler functions. This problem is ill-posed, i.e. the solution(if exists) does not depend on the measurable data. Three different kinds landweber iterative methods are used to solve this problem. Under the priori and the posteriori regularization parameters choice rules, the error estimates between the exact solution and the regularization solutions are obtained. Several numerical examples are given to prove the effectiveness of these regularization methods.

Automated summary

This paper investigates the inverse problem of identifying the initial value of time-fractional diffusion wave equation on a spherically symmetric region, obtaining the exact solution through variable separation and Mittag-Leffler functions and using three different Landweber iterative methods for solving. The effectiveness of the regularization methods is demonstrated through several numerical examples.