Geodesic
Stability of two-layer operator-difference schemes with symmetric and skew-symmetric operators
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 979-991.

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Two-layer operator-difference schemes with weight parameters which contain symmetric and skew-symmetric operators are considered. Sufficient conditions and a priori estimates for stability are derived using the method of reduction to a three-layer operator-difference scheme. It is shown that the conditions are necessary ones for some particular cases. The results may be used for investigation of the grid problems approximating initial-boundary value problems of mathematical physics with convection transfer (of convection-diffusion type), including the problems with varying coefficients on various grids. 
@article{FPM_1999_5_4_a1,
     author = {N. V. Ardelyan},
     title = {Stability of two-layer operator-difference schemes with symmetric and skew-symmetric operators},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {979--991},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a1/}
}
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N. V. Ardelyan. Stability of two-layer operator-difference schemes with symmetric and skew-symmetric operators. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 979-991. http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a1/