Central difference schemes in time and error estimate on a non-standard inverse heat conduction problem

摘要

Inverse heat conduction problems (IHCP) are severely ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. But now the results available in the literature on IHCP are mainly devoted to the standard sideways heat equation. This paper remedies this by a central difference schemes in time which itself has a regularizing effect for a non-standard IHCP which appears in some applied subjects. An error estimate is obtained and the error estimate also gives information about how to choose the step length in the time discretization. A numerical example shows that the computational effect of this method is satisfactory.