New fast iteration for determining surface temperature and heat flux of general sideways parabolic equation. (English) Zbl 1205.35337
Summary: The inverse heat conduction problem (IHCP) in the quarter plane, where data are given at \(x=1\), is called sideways parabolic equation and is severely ill-posed. Numerical methods such as Tikhonov, Fourier and wavelet regularization methods have been developed. However, they contain an a priori bound of the solution in their parameter choice. A large estimate bound may cause bad numerical results. In this paper, we introduce a new class of iteration methods to solve the IHCP and prove that our methods are of order optimal under both a priori and a posteriori stopping rules. An appropriate selection of a parameter in the iteration scheme helps to reduce the iterative steps and to get a satisfactory approximate solution. Furthermore, if we use the discrepancy principle, we can avoid the selection of an a priori bound.
MSC:
| 35R30 | Inverse problems for PDEs |
| 80A23 | Inverse problems in thermodynamics and heat transfer |
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65T60 | Numerical methods for wavelets |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
Keywords:
inverse heat conduction problem; sideways parabolic equation; heat flux; iteration; discrepancy principleReferences:
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