A COMPARISON OF REGULARIZATIONS FOR AN ILL-POSED PROBLEM

We consider numerical methods for a ''quasi-boundary value'' regulariz ation of the backward parabolic problem given by [GRAPHICS] where A is positive self-adjoint and unbounded. The regularization, due to Clark and Oppenheimer, perturbs the final value u(T) by adding alpha u(0), where a is a small parameter. We show how this leads very naturally to a reformulation of the problem as a second-kind Fredholm integral equ ation, which can be very easily approximated using methods previously developed by Ames and Epperson. Error estimates and examples are provi ded. We also compare the regularization used here with that from Ames and Epperson.