Abstract
Boundary-value problems for an equation of parabolic type, in which the coefficient of the highest-order derivatives involves a parameter varying in the half-open interval (0,1], are considered. As the parameter approaches zero, parabolic boundary layers develop near the boundary of the domain. It is shown that the attempt to use adjustive methods to construct difference schemes that are uniformly convergent (with respect to the parameter) for such systems meets certain difficulties; in fact, for uniform grids there is no such adjustive scheme. A study is presented of two problems for a parabolic equation with mixed derivatives: a periodic boundary-value problem in a strip and the Dirichlet problem in a two-dimensional domain whose boundary is a smooth curve. In both cases it is possible to construct difference schemes that converge uniformly in the parameter throughout the domain.
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