Geodesic
On the application of nonstationary form of the Tappert equation as an artificial boundary condition
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 2, pp. 191-206.

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In this paper, a nonstationary analog of the range refraction parabolic equation is derived. A new approach to the derivation of Tappert's operator asymptotic formula with the use of noncommutative analysis is presented. The obtained nonstationary equation is proposed as an artificial boundary condition for the wave equation in underwater acoustics. This form of artificial boundary condition has low computational cost and systematically takes into account variations of sound speed. This is confirmed by various numerical experiments, including propagation of normal modes and wave fields produced by point source. 
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M. Yu. Trofimov; P. S. Petrov. On the application of nonstationary form of the Tappert equation as an artificial boundary condition. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 2, pp. 191-206. http://geodesic.mathdoc.fr/item/FPM_2009_15_2_a8/

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