Numerical procedures for the determination of the leading coefficient a ( x )

The aim of this paper 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 finite difference methods, backward Euler and Crank–Nicolson schemes are studied. The results of a numerical example are presented, which demonstrate the efficiency and rapid convergence of the methods. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)