M. M. Institute of Applied Mathematics In. Keldysh Academy of Sciences of the USSR . Preprint No. 111 for 1990 . - 24 s. , OCR. On the example of the model boundary problem for the parabolic equation of the second order, the main approaches to the approximate solution of unstable problems of mathematical physics by difference methods are considered .. Incorrectness of the problem is due to the instability of the solution of relatively small perturbations of the initial condition. The work focuses on the regularization of difference schemes. The study of the stability of the corresponding difference schemes is carried out on the basis of the general results of the theory of ro-stability of difference schemes .. This mathematical apparatus most fully conveys the specifics of the considered incorrect evolutionary problems. The regularization of difference schemes corresponds at the differential level to the use of some (known and unknown) variants of the quasi-conversion method.