Abstract
The first boundary-value problem for a parabolic equation is considered in a finite interval. The highest-order derivative contains a parameter which takes arbitrary values in the half-open interval (0, 1]; the coefficients and the free term in the equation have discontinuities of the first kind at a finite number of points. Concentrated factors (sources, etc) may also act at these points. The appearance of concentrated “thermal resistances” produces discontinuities of the first kind in the solutions. A difference scheme uniformly convergent in the parameter everywhere in a given region is constructed for solving the boundary-value problem using grids with condensation in the boundary and transition layers.
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