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Rational approximations to \(1/ \sqrt {1-s^ 2}\), one-way wave equations and absorbing boundary conditions. (English) Zbl 0860.65072

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.

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
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References:

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