A direct numerical method for solving inverse heat source problems

Abstract

Inverse source problems is a classical ill-posed problem. There exist several literatures on inverse heat source problems. In this study we use some stable methods to deal with the inverse problems of determining space-wise and time-wise dependent heat source in the heat diffusion equation. The problems of inverse heat source sources are transferred to the problems of numerical differentiation. By simple and effective methods which are used to regularize the problems of numerical differentiation before, we can obtain stable solutions. The numerical results show that our proposed procedure yields stable and accurate approximation.