Geodesic
Mathematical simulation of acoustic wave refraction near a caustic
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 7, pp. 1124-1138

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Issues related to the computation of wave fields in an acoustic medium near caustics are considered. A boundary condition on a caustic is established, and the Green’s function of a boundary value problem for the general case of a varying speed of sound is constructed. For this purpose, an auxiliary Goursat problem is considered and a system of its particular solutions is constructed using hypergeometric functions. A Volterra integral equation for the Green’s function is obtained, and an algorithm for its expansion with respect to smoothness is described. A finite difference scheme approximating the solution of the differential problem with an unbounded coefficient is proposed. Numerical results are presented. 
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     author = {A. V. Baev},
     title = {Mathematical simulation of acoustic wave refraction near a caustic},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1124--1138},
     publisher = {mathdoc},
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     number = {7},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_7_a8/}
}
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A. V. Baev. Mathematical simulation of acoustic wave refraction near a caustic. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 7, pp. 1124-1138. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_7_a8/