An stable numerical algorithm for identifying the solution of an inverse problem

In this paper, we consider an inverse parabolic problem with space dependent coefficient. Mathematical model of the problem consists a parabolic equation in which the condition is unknown at the one of the boundary and to be determined from an overspecified data measured at an interior point inside the body. Uniqueness of the solution of under study inverse problem will be shown. Our concern for the numerical procedure for this inverse problem is based on a finite differences scheme. Stability conditions for numerical solution to inverse problem are stated. The approach of proposed method is approximated the unknown function by a set of Chebyshev polynomials, where the unknown set of expansion coefficients in unknown function are determined from the minimizing the least squares method. Some numerical examples will be given in the last section.