Graduate School of Mathematical Sciences Komaba, Tokyo, Japan Reconstruction of a Moving Boundary from Cauchy Data in One Dimensional Heat Equation
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چکیده
In this paper, we propose a new numerical method for determining a moving boundary from Cauchy data in one dimensional heat equation. The numerical scheme is based on the use of fundamental solutions of the heat equation as basis functions. In order to regularize the ill-conditioned linear system of equations resulted by collocating boundary data, we apply successfully the Tikhonov regularization with the generalized cross validation parameter choice rule to obtain a stable numerical approximation to a moving boundary.
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