Numerical method for solving the inverse heat transfer boundary value problem with incomplete data

We proposed a numerical method for solving the inverse heat conduction problem with incomplete data. The problem addresses heat transfer in a homogeneous object whose surface experiences uniform external thermal action. The model is formulated as an inverse heat conduction problem for a onedimensional parabolic partial differential equation, incorporating an initial condition and a single boundary condition. The boundary condition relies on temperature measurements taken at the object's surface. Our approach utilizes a computational finite-difference scheme to solve the inverse problem, with regularization techniques ensuring numerical stability. The discretization steps serve as the regularization parameter. To assess the reliability of the proposed method and estimate the numerical error, we conducted computational experiments. These experiments included a comparative analysis of the numerical results against test functions. The computational findings demonstrate the feasibility of numerically solving inverse problems with incomplete data and confirm the sufficient reliability of the proposed approach.