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

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.