The Inverse Problem Of Determining The Unknown Source Term In A Heat Equation

Determining the unknown source term in a heat equation is a class of inverse problem with important application background, which is Ill-posed in the sense of Hadamard. In this article, we will discuss the ways of how to get their stable numerical solutions, in which the continous and discrete regularization method, with and without knowing the error level 6 of input data, are presented and a regularization strategy based on linear approximation for identifying the nonlinear source term is also given. The theoritical analysis and numerical testing results indicate that the algorithm proposed in this paper is stable and effective.