COMPARISON BETWEEN THE KRYLOV SUBSPACE METHOD AND THE TRUNCATION METHOD FOR IDENTIFYING AN UNKNOWN SOURCE IN THE HEAT EQUATION

Abstract

In this paper, we are concerned with the problem of approximating a solution of an inverse parabolic problem. In order to overcome the instability of the original problem, we use the troncature spectral method to construct a stable approximate solution. To calculate the stabilized solution, we use a numerical procedure based on the Krylov subspace method. This algorithm provides us a practical and simple method to calculate numerically the stabilized solution. Some Numerical tests are presented to illustrate the accuracy and efficiency of this method.