The boundary element method for the solution of the backward heat conduction equation

In this paper we consider the numerical solution of the one-dimensional, unsteady heat conduction equation in which Dirichlet boundary conditions are specified at two space locations and the temperature distribution at a particular time, say T0, is given. The temperature distribution for all times, t 0, is now required and this backward heat conduction problem is a well-known improperly posed problem. In order to solve this problem the minimal energy technique has been introduced in order to modify the boundary element method and this results in a stable approximation to the solution and the accuracy of the numerical results are very encouraging. Copyright © 1995 Academic Press. All rights reserved.