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Central difference schemes in time and error estimate on a non-standard inverse heat conduction problem. (English) Zbl 1068.65117

Authors’ summary: Inverse heat conduction problems (IHCP) are severely ill-posed in the sense that the solution (if it exists) does not depend continuously on the standard sideways heat equation. This paper remedies this by a central difference scheme 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.

MSC:

65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R30 Inverse problems for PDEs
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