Chebyshev Polynomial Regularization Method For Solving Two Kinds Of Inverse Source Problems

The unknown source problem of Poisson equation and the source identification problem of time-fractional diffusion equation are two kinds of ill-posed problems.This paper considers that the Chebyshev polynomial regularization method Compared with the classical Tikhonov regularization method,this method has no saturation restriction and better convergence.Chebyshev polynomial regularization method is less used to solve the inverse problem,and they are all theoretically for the case of compact operator Kx=y.In this paper,the Chebyshev polynomial regularization method is used to solve two kinds of specific inverse source problems,and the error estimates under the prior and posterior regularization parameter selection rules are given.Furthermore,numerical results show that the Chebyshev polynomial regularization method provided is effective and feasible.