Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 51, pp. 1-14.
Title: Regularization of a discrete backward problem
using coefficients of truncated Lagrange polynomials
Authors: Duc Trong Dang (Hochiminh City National Univ., Vietnam)
Ngoc Lien Tran (Cantho Univ., Cantho, Vietnam)
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.