A numerical solution of an inverse parabolic problem

In this paper, we will first study the existence and uniqueness of the solution of an inverse problem for a linear equation with non-linear boundary conditions (radiation terms), via an auxiliary problem. Furthermore, a stable numerical algorithm based on the use of the solution to the auxiliary problem as a basis function is proposed. To regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization method to obtain the stable numerical approximation to the solution. Some numerical experiments confirm the utility of this algorithm as the results are in good agreement with the exact data.Publisher's Versio