Numerical solution for an inverse heat source problem by an iterative method

In this paper, we consider a typical inverse heat source problem, that is, we determine two separable source terms in a heat equation from the initial and boundary data along with two additional measurements. By a simple transformation, the original problem is changed into a nonlinear problem, and then we use an iterative method to solve it. After giving an algorithm, we prove some Hölder convergence rates for both the reconstructed heat source terms and the temperature distribution subject to certain bounds of the data. Numerical results show that our method is accurate and efficient.