Renaut, R. A.; Parent, J. S. Rational approximations to \(1/ \sqrt {1-s^ 2}\), one-way wave equations and absorbing boundary conditions. (English) Zbl 0860.65072 J. Comput. Appl. Math. 72, No. 2, 245-259 (1996). One-way wave equations (OWWEs), derived from rational approximations \(C(s)\) to \(1/\sqrt{1-s^2}\) are considered. Absorbing boundary conditions obtained from these OWWEs are easily implemented, producing systems of differential equations at the boundary. These equations are different from those obtained by rational approximations \(r(s)\) to \(\sqrt{1-s^2}\). However a particular choice of difference approximation for the system yields numerical methods such that stability properties of both approaches are equivalent.Numerical results are presented which demonstrate that in some cases the \(C(s)\) OWWEs can provide better absorption. Reviewer: Z.Dżygadło (Warszawa) Cited in 1 Document MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 41A20 Approximation by rational functions 35L05 Wave equation 86-08 Computational methods for problems pertaining to geophysics 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 86A15 Seismology (including tsunami modeling), earthquakes Keywords:numerical examples; one-way wave equations; absorbing boundary conditions; difference approximation; stability PDFBibTeX XMLCite \textit{R. A. Renaut} and \textit{J. S. Parent}, J. Comput. Appl. Math. 72, No. 2, 245--259 (1996; Zbl 0860.65072) Full Text: DOI References: [1] Claerbout, J. F., Imaging the Earth’s Interior (1985), Blackwell: Blackwell Oxford [2] Clayton, R. W.; Engquist, B., Absorbing boundary conditions for acoustic and elastic wave equations, Bull. Seis. Soc. Amer., 67, 1529-1540 (1977) [3] Collino, F., High order absorbing boundary conditions for wave propagation models: straight line and corner cases, (Kleinman, R.; etal., Mathematical and Numerical Aspects of Wave Propagation (1993), SIAM: SIAM Philadelphia, PA), 161-171 · Zbl 0814.35065 [4] Gustafsson, B.; Kreiss, H. O.; Sundström, A., Stability theory of difference approximations for mixed initial boundary value problems, II, Math. Comput., 26, 649-686 (1972) · Zbl 0293.65076 [5] Halpern, L.; Trefethen, L. N., Wide-angle one-way wave equations, J. Acoust. Soc. Amer., 84, 1397-1404 (1988) [6] Henrici, P., (Applied and Computational Complex Analysis, I (1974), Wiley: Wiley New York), 491-493 [7] Lindman, E. L., Free space boundary conditions for the time dependent wave equation, J. Comput. Phys., 18, 66-78 (1975) · Zbl 0417.73042 [8] Parent, J. S., Absorbing boundaries for the two-dimensional acoustic wave equation, (Master’s Thesis (1991), Dept. of Mathematics, Arizona State University) [9] Renaut, R. A., Absorbing boundary conditions, difference operators and stability, J. Comput. Phys., 102, 236-251 (1992) · Zbl 0766.65070 [10] Renaut, R. A., Absorbing boundary conditions for acoustic and elastic waves, (Baines, M. J.; Morton, K. W., Numerical Methods for Fluid Dynamics (1993), Oxford University Press: Oxford University Press New York), 491-498 · Zbl 0802.76049 [11] Renaut, R. A.; Fröhlich, J., A pseudospectral Chebychev method for the 2D wave equation with domain stetching and absorbing boundary conditions, J. Comput. Phys. (1996), to appear · Zbl 0849.65079 [12] Renaut, R. A.; Parent, J., Rational approximations, one way wave equations and absorbing boundary conditions, (Technical Report #135 (1992), Arizona State University) · Zbl 0860.65072 [13] Renaut, R. A.; Peterson, J., Stability of wide-angle absorbing boundary conditions for the wave equation, Geophysics, 54, 1153-1163 (1989) [14] Tappert, F. D., The parabolic approximation method, (Keller, J. B.; Papadakis, J. S., Wave Propagation and Underwater Acoustics. Wave Propagation and Underwater Acoustics, Lecture Notes in Physics, Vol. 70 (1977), Springer: Springer Berlin), 224-287 [15] Trefethen, L. N.; Halpern, L., Well-posedness of one-way wave equations and absorbing boundary conditions, Math. Comput., 47, 421-435 (1986) · Zbl 0618.65077 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.