A numerical approximation to the solution of an inverse heat conduction problem

The aim of this article is to study the parabolic inverse problem of determination of the leading coefficient in the heat equation with an extra condition at the terminal. After introducing a new variable, we reformulate the problem as a nonclassical parabolic equation along with the initial and boundary conditions. The uniqueness and continuous dependence of the solution upon the data are demonstrated, and then finite difference methods, backward Euler and Crank–Nicolson schemes are studied. The results of some numerical examples are presented to demonstrate the efficiency and the rapid convergence of the methods. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010