New fast iteration for determining surface temperature and heat flux of general sideways parabolic equation

The inverse heat conduction problem (IHCP) in the quarter plane, where data are given at x=1x=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 the 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 will help reduce the iterative steps and get a satisfactory approximate solution. Furthermore, if we use the discrepancy principle we can avoid the selection of the a priori bound.