An iterative generalized quasi-boundary value regularization method for the backward problem of time fractional diffusion-wave equation in a cylinder

In this paper, we consider the backward problem for a time fractional diffusion-wave equation in a cylinder. The ill-posedness and a conditional stability of the inverse problem are proved. Based on the generalized quasi-boundary value regularization method, we propose an iterative generalized quasi-boundary value regularization method to deal with the inverse problem, and this iterative method has a higher convergence rate. The convergence rates of the regularized solution under an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule are obtained. Numerical examples illustrate the effectiveness and stability of our proposed method.

Automated summary

In this paper, the backward problem for a time fractional diffusion-wave equation in a cylinder is considered. The ill-posedness and conditional stability of the inverse problem are proved. An iterative generalized quasi-boundary value regularization method is proposed based on the generalized quasi-boundary value regularization method, which shows a higher convergence rate. The convergence rates of the regularized solution under both a priori and a posteriori regularization parameter choice rules are obtained. Numerical examples demonstrate the effectiveness and stability of the proposed method.