Abstract: The sideways problem of nonhomogeneous heat equation is discussed, which is seriously ill-posed. By using the iterative regularization method, a regular approximate solution of the problem is obtained, and the Hlder type error estimate of this solution relative to the exact solution is given under a prior and a posterior regularization parameter selection rules, which shows that the iterative regularization method is effective to solve such problems.

Key words: inhomogeneous heat equation;sideways problem, ill-posed, iterative regularization, error estimate