Geodesic
Nonreflecting artificial boundary conditions for change of omitted equations with lacunas
Matematičeskoe modelirovanie, Tome 12 (2000) no. 12, pp. 108-127.

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Artificial boundary conditions (ABC) are constracted which are equivalent to 3D-wave equation outside of unit sphere. The algorithm for using this ABC is also suggested. It demonstrates the ABC and algorithm are effective for calculations on long time. The ABC and algorithm are based on the method of difference potentials and lacunas of 3D-wave equation solutions. 
@article{MM_2000_12_12_a8,
     author = {V. S. Ryaben'kii and V. I. Turchaninov and S. V. Tsynkov},
     title = {Nonreflecting artificial boundary conditions for change of omitted equations with lacunas},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {108--127},
     publisher = {mathdoc},
     volume = {12},
     number = {12},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2000_12_12_a8/}
}
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V. S. Ryaben'kii; V. I. Turchaninov; S. V. Tsynkov. Nonreflecting artificial boundary conditions for change of omitted equations with lacunas. Matematičeskoe modelirovanie, Tome 12 (2000) no. 12, pp. 108-127. http://geodesic.mathdoc.fr/item/MM_2000_12_12_a8/