On the locally one-dimensional schemes for solving the third boundary value parabolic problems in nonrectangular domains

The paper deals with studying some modifications of the local one-dimensional schemes for solving the mixed and the third boundary value parabolic problems in nonrectangular domains. Contrary to the usual schemes with the error estimate $O(h+\tau/\sqrt h)$, these modifications have unconditional convergence with the error estimate $O(h+\tau)$ for the problem with the mixed boundary conditions of special type and $O(h+\tau^{5/6})$ for the third boundary value problem.