Abstract
In this paper, we introduce a modified Landweber iteration to solve the sideways parabolic equation, which is an inverse heat conduction problem (IHCP) in the quarter plane and is severely ill-posed. We shall show that our method is of optimal order under both a priori and a posteriori stopping rule. Furthermore, if we use the discrepancy principle we can avoid the selection of the a priori bound. Numerical examples show that the computation effect is satisfactory.
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Supported by the National Natural Science Foundation of China (No. 10971019) and Scientific Research Fund of Guangxi Education Department Grant No. 201012MS067.
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Liu, Jb., Deng, Yj. A modified Landweber iteration for general sideways parabolic equations. Acta Math. Appl. Sin. Engl. Ser. 27, 727–738 (2011). https://doi.org/10.1007/s10255-011-0104-8
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DOI: https://doi.org/10.1007/s10255-011-0104-8