Two regularization methods and the order optimal error estimates for a sideways parabolic equation

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Abstract

In this paper, we consider an inverse heat conduction problem which appears in some applied subjects. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. A Tikhonov type's regularization method and a Fourier regularization method are applied to formulate regularized solutions which are stably convergent to the exact ones with order optimal error estimates. A numerical example shows that the computational effect of these methods are all satisfactory. © 2005 Elsevier Ltd. All rights reserved.

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Fu, P., Fu, C. L., Xiong, X. T., & Li, H. F. (2005). Two regularization methods and the order optimal error estimates for a sideways parabolic equation. Computers and Mathematics with Applications, 49(5–6), 777–788. https://doi.org/10.1016/j.camwa.2004.08.012

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