Numerical Reconstruction of Heat Source on a Semi-Infinite Rod

Inverse heat conduction on an unbounded domain has always been the focus and difficulty in engineering and mechanical fields. In this paper, we consider the inverse problem of identifying the heat source by using the terminal measured temperature data. Being different from other ordinary heat conduction problems, our mathematical model is defined in a semi-infinite region, which may lead to many numerical methods that cannot be used directly. Based on the artificial boundary method, we first introduce the truncated boundary and derive the exact boundary conditions on it. Then we use the finite difference method to establish an approximate difference scheme for the forward problem. For the inverse problem, we design the Landweber and conjugate gradient iterative algorithm and do numerical experiments. Numerical results verify the correctness and effectiveness of our algorithm.