INVERSE PROBLEM OF ONE DIMENSIONAL HEAT EQUATION WITH TIKHONOV REGULARIZATION METHOD - Ronaldo Mulia, Kelvin
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.