A NEW ITERATION ALGORITHM WITH RELAXATION FACTOR FOR THE CAUCHY PROBLEM OF TIME-FRACTIONAL DIFFUSION EQUATION

In this paper, we investigate a Cauchy problem for the time-fractional diffusion equation by using a new simplified iteration algorithm. The algorithm arises from the well-known Kozlov-Maz'ya iterative scheme for solving the Cauchy problem of classical ill-posed boundary value problems. A relaxation factor in the algorithm is introduced. Based on Fourier analysis, we give a choice rule for the relaxation factor. The iteration algorithm combined with a stopping criterion is given for stable numerical reconstruction of the solution. For illustration, several numerical experiments are constructed to demonstrate the feasibility and efficiency of the proposed method.