Boundary inverse heat conduction problem: algorithm and error analysis

Abstract

Methods based on solving boundary inverse heat conduction problems are widely used at present in experimental investigations of thermal processes between solids and the environment. An iterative regularization method is used in the presented paper to solve ill-posed inverse problems. The method is based on minimizing the residual functional by means of gradient methods of the first kind and spline-approximation of unknown functions. An optimal number of approximation parameters using the residual principle is chosen. The accuracy of the solution of inverse problems obtained by the suggested algorithms is discussed.