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

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.

Show me the PDF file (250K), TEX file, and other files for this article.

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

Return to the EJDE web page