Electron. J. Diff. Eqns., Vol. 2007(2007), No. 51, pp. 1-14.

Regularization of a discrete backward problem using coefficients of truncated Lagrange polynomials

Duc Trong Dang, Ngoc Lien Tran

Abstract:
We consider the problem of finding the initial temperature $u(x,0)$, from a countable set of measured values $\{ u(x_j,1)\}$. The problem is severely ill-posed and a regularization is in order. Using the Hermite polynomials and coefficients of truncated Lagrange polynomials, we shall change the problem into an analytic interpolation problem and give explicitly a stable approximation. Error estimates and some numerical examples are given.

Submitted December 30, 2006. Published April 5, 2007.
Math Subject Classifications: 30E05, 33C45, 35K05.
Key Words: Discrete backward problem; truncated Lagrange polynomial; Hermite polynomial; interpolation problem.

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Duc Trong Dang
Department of Mathematics and Computer Sciences
Hochiminh City National University
227 Nguyen Van Cu, Hochiminh City, Vietnam
email: ddtrong@mathdep.hcmuns.edu.vn
Ngoc Lien Tran
Faculty of Sciences, Cantho University
Cantho, Vietnam
email: tnlien@ctu.edu.vn

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