INVERSE PROBLEM OF ONE DIMENSIONAL HEAT EQUATION WITH TIKHONOV REGULARIZATION METHOD
This article discusses two inverse problems of one-dimensional heat equation. First problem related to information of the temperature at one location in various time. Based on this information, we will determine the boundary condition of heat dierential equation problem. Integral equation is cons...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/34146 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | This article discusses two inverse problems of one-dimensional heat equation.
First problem related to information of the temperature at one location in
various time. Based on this information, we will determine the boundary condition
of heat dierential equation problem. Integral equation is constructed
from the heat equation to solve this problem. However, the backward heat
conduction problem is an ill-posed problem, and this inverse problem is illposed
too. Some regularization methods will be used to solve this problem.
[1]
The second problem related to information of nal temperature at all location.
This problem is an extension of [6] which discusses the one-dimensional inverse
problem throughout all the area. In this article, we discuss the similar issue
that is dened on the half line. The boundary condition will be exist and
Cosine Fourier transform will be applied to the heat equation.
We will use Tikhonov regularization method to solve this inverse problem.
Numerical tests show the error between the approximation solution with the
analytic solution. |
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