The use of special transformations in the numerical solution of boundary layer problems

Estimates of the derivatives are obtained for certain boundary-layer problems, making it possible to isolate singularities of the solutions effectively. On the basis of these estimates special transformations, which smooth out the singularities, are constructed. These transformations are used to construct numerical algorithms for solving certain problems in which the coefficient of the highest-order derivative is a small parameter. It is proved that the numerical solution converges uniformly to the exact solution.