Geodesic
On the locally one-dimensional schemes for solving the third boundary value parabolic problems in nonrectangular domains
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 4, pp. 347-362

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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. 
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     author = {Yu. M. Laevsky and O. V. Rudenko},
     title = {On the locally one-dimensional schemes for solving the third boundary value parabolic problems in nonrectangular domains},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {347--362},
     publisher = {mathdoc},
     volume = {1},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1998_1_4_a5/}
}
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Yu. M. Laevsky; O. V. Rudenko. On the locally one-dimensional schemes for solving the third boundary value parabolic problems in nonrectangular domains. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 4, pp. 347-362. http://geodesic.mathdoc.fr/item/SJVM_1998_1_4_a5/