A stable numerical algorithm for solving an inverse parabolic problem

Abstract

In this paper we consider a numerical approach for the determination of an unknown boundary condition in the inverse heat conduction problem (IHCP). The given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. The numerical algorithm based on finite-difference method and the least-squares scheme for solving the inverse problem. To regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization method with L- curve scheme to obtain the stable numerical approximation to the solution.