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Simultaneous determination of source term and initial value in the heat conduction problem by modified quasi-reversibility regularization method.
- Source :
-
Numerical Heat Transfer: Part B -- Fundamentals . 2022, Vol. 82 Issue 3/4, p112-127. 16p. - Publication Year :
- 2022
-
Abstract
- In this article, we investigate the inverse problem of determining source term and initial data simultaneously in a parabolic equation where data are given at two fixed times. We can get the exact solution of the problem by the Fourier transform, and find that the problem is ill-posed, i.e., the solution does not depend continuously on the input data and small errors in the data can destroy the numerical solution. Hence, a modified quasi-reversibility regularization method is used to solve the problem and an order-optimal error estimate is obtained under a suitable parameter choice rule. Finally, some numerical examples including smooth and nonsmooth functions show that the proposed method is effective and stable. [ABSTRACT FROM AUTHOR]
- Subjects :
- *HEAT conduction
*SMOOTHNESS of functions
*FOURIER transforms
*PROBLEM solving
Subjects
Details
- Language :
- English
- ISSN :
- 10407790
- Volume :
- 82
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Numerical Heat Transfer: Part B -- Fundamentals
- Publication Type :
- Academic Journal
- Accession number :
- 158860087
- Full Text :
- https://doi.org/10.1080/10407790.2022.2079281