A numerical method consists of combining the Haar basis method and the Tikhonov regularization method. We apply the method to solve some inverse problems for two-dimensional 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,z) at a point x=a, 0<a<1. We also show that the rate of convergence of the method is 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.