Geodesic
Finite difference method in the problem of diffraction of a plane acoustic wave in a half-plane with a cut
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 12, pp. 2214-2231 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the numerical solution of the diffraction problem for an acoustic plane wave in a half-plane with a cut, boundary conditions that are equivalent to the radiation conditions at infinity are set in a neighborhood of the points of the cut. Joining the physical boundary conditions on the cut, a closing set of equations of order $4N$, where $N$ is the number of grid points on the cut, is obtained. The so-called Green's grid function for the half-plane is used, which makes it possible to pass from one grid layer to another one for the solution satisfying certain conditions at infinity. 
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     title = {Finite difference method in the problem of diffraction of a~plane acoustic wave in a~half-plane with a~cut},
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A. O. Rodnikov; B. A. Samokish. Finite difference method in the problem of diffraction of a plane acoustic wave in a half-plane with a cut. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 12, pp. 2214-2231. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_12_a10/

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