Geodesic
Spectral approach to the construction of the non-reflecting boundary conditions
Matematičeskoe modelirovanie, Tome 13 (2001) no. 11, pp. 23-47.

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Spectral approach is proposed for the effective approximation of the accurate nonreflecting artificial boundary conditions which equivalently substitute linear homogeneous difference equations outside the bounded computational subdomain for non-stationary problems. Basic idea is primarily illustrated by the simple example and then the ways of generalization are proposed. Application of the spectral approach is based upon the difference potentials method. Necessary results concerning this method are presented here independently on the original papers. 
@article{MM_2001_13_11_a2,
     author = {V. S. Ryaben'kii and V. I. Turchaninov},
     title = {Spectral approach to the construction of the non-reflecting boundary conditions},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {23--47},
     publisher = {mathdoc},
     volume = {13},
     number = {11},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2001_13_11_a2/}
}
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V. S. Ryaben'kii; V. I. Turchaninov. Spectral approach to the construction of the non-reflecting boundary conditions. Matematičeskoe modelirovanie, Tome 13 (2001) no. 11, pp. 23-47. http://geodesic.mathdoc.fr/item/MM_2001_13_11_a2/