Haar basis method to solve some inverse problems for two-dimensional parabolic and hyperbolic equations

Abstract

A numerical method consists of combining Haar basis method and Tikhonov regularization method. We apply the method to solve some inverse problems for twodimensional parabolic and hyperbolic equations using noisy data. In this paper, a stable numerical solution of these problems is presented. This method uses a sensor located at a point inside the body and measures the u(x; y; t) at a point x = a; 0 < a < 1. We also show that the rate of convergence of the method is as exponential. Numerical results show that a good estimation on the unknown functions of the inverse problems can be obtained within a couple of minutes CPU time at Pentium IV-2.53 GHz PC.