Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space (Journal of Partial Differential Equations, 2020)
" In this paper we consider a semi-descretization difference scheme for solving a Cauchy problem of heat equation in two-dimensional setting. Some error estimates are proved for the semi-descretization difference regularization method which cannot be fitted into the framework of regularization theory presented by Engl, Hanke and Neubauer. Numerical results show that the proposed method works well."
Keywords: 2D inverse heat conduction problem; Ill-posedness; regularization; error estimate; finite difference