Central difference regularization method for identifying heat source in parabolic equation

The inverse problem of heat source identification of a class of parabolic equations with spatial variable alone was discussed.This problem was ill-posed,i.e.the solution does not depend continuously on the data measured.A regularization approximate solution of the inverse problem was obtained by using central difference regularization method and it was given that there was Hlder type stability estimate between the regularization solution and exact solution.Several numerical examples showed that the central difference regularization method would work effectively for identifying the heat source.