Geodesic
Regularization difference schemes for the equations with nonselfadjoint operators
Matematičeskoe modelirovanie, Tome 4 (1992) no. 2, pp. 36-44.

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Principle of difference schemes regularization is developed for two- layers difference schemes with nonselfadjoint difference operators. A common boundary problem for a second order parabolic equation with nonselfadjoint elliptic operator is considered. Stable difference schemes with different types of regularizators are constructed. Investigation of regularized difference schemes is based on an appropriate energetic identity. Sufficient conditions of stability of two- layer difference schemes with nonselfadjoint operators are obtained. Difference schemes for incorrect parabolic problem with reversed time are treated as the second example. Appropriate $\rho$-stable difference schemes are investigated. 
@article{MM_1992_4_2_a3,
     author = {A. A. Samarskii and P. N. Vabishchevich},
     title = {Regularization difference schemes for the equations with nonselfadjoint operators},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {36--44},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1992_4_2_a3/}
}
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A. A. Samarskii; P. N. Vabishchevich. Regularization difference schemes for the equations with nonselfadjoint operators. Matematičeskoe modelirovanie, Tome 4 (1992) no. 2, pp. 36-44. http://geodesic.mathdoc.fr/item/MM_1992_4_2_a3/