It is well known that the backward heat conduction problem is a severely

ill-posed problem. To show the influence of the final time values [T.sub.1] and [T.sub.2] on the numerical inversion results, we solve the inverse problem in Examples 1 and 2 by our proposed method with different large final time values and fixed values n = 200, m = 20, and [delta] = 0.10.

Following [21], as a severely

ill-posed problem we will understand the equation (1.1) for which a kernel of A is much smoother than the solution of (1.1).

As mentioned above, this problem is coupled by a severely

ill-posed problem and a mildly ill-posed one.

The continuation problem is

ill-posed problem; its solution is unique, but it does not depend continuously on the Cauchy data [1-10].

Stanculescu, Iuliana, University of Pittsburgh, Turbulence modeling as an

ill-posed problem.

This is an

ill-posed problem, and there are several difficulties connected with the solution of these problems (1,2).

Therefore the backward identification problem is an

ill-posed problem.

It is obvious that for this highly

ill-posed problem the OGSDA is convergent fast, and accurate.

The exponentially ill-posed operator yields under the assumption of a particularly smooth exact solution a moderately

ill-posed problem. Therefore, it appears to be impossible to infer the smoothness of both the operator and solution from a given convergence rate without a priori knowledge of the type of smoothness of these objects.

In the second example, we discuss an

ill-posed problem where the condition number of linear operator A is 255; we aim to demonstrate that the proposed method is stable even with large condition numbers.

In addition, as we know, for

ill-posed problem, the regularization parameter a plays an important role and hence has to be chosen appropriately.