Geodesic
On patterns of the method of lines of high accuracy for some two-dimensional parabolic equations
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part X, Tome 219 (1994), pp. 81-93

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An application of the method of lines to the first mixed problem for two-dimensional half-linear and linear parabolic equations denned in a cylindrical domain with a rectangular foundation is considered. For the half-linear equation the scheme of an accuracy $O(h^3)$ is constructed. For the linear equation with the coefficients being functions only of time $t$ the scheme of any accuracy for corresponding accuracy of approximation is constructed. Bibliography: 7 titles. 
@article{ZNSL_1994_219_a3,
     author = {A. P. Kubanskaya},
     title = {On patterns of the method of lines of high accuracy for some two-dimensional parabolic equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {81--93},
     publisher = {mathdoc},
     volume = {219},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_219_a3/}
}
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A. P. Kubanskaya. On patterns of the method of lines of high accuracy for some two-dimensional parabolic equations. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part X, Tome 219 (1994), pp. 81-93. http://geodesic.mathdoc.fr/item/ZNSL_1994_219_a3/