TY - JOUR
T1 - Rational approximations to 1/√1 - s2, one-way wave equations and absorbing boundary conditions
AU - Renaut, Rosemary
AU - Parent, J. S.
N1 - Funding Information:
* Corresponding author: e-mail: renaut@math.la.asu.edu. I The work of the first author was supported by National Science Foundation grant ASC 8812147 and American Chemical Society Petroleum Research Fund grant 20681-92.
PY - 1996/8/13
Y1 - 1996/8/13
N2 - One-way wave equations (OWWEs), derived from rational approximations, C(s) to 1/√1 - s2, are considered. Absorbing boundary conditions obtained from these OWWEs are easily implemented, producing systems of differential equations at the boundary which are different from those produced by rational approximations, r(s) to √1 - s2. Although these systems are different, a particular choice of difference approximation for the system yields numerical methods such that stability properties of both approaches are equivalent. In particular, for C(s) = 1/r(s), the two systems possess equivalent stability properties. In other cases, numerical results are presented which demonstrate that, where C(s) and r(s) are not derived via interpolation, the C(s) OWWEs can provide better absorption.
AB - One-way wave equations (OWWEs), derived from rational approximations, C(s) to 1/√1 - s2, are considered. Absorbing boundary conditions obtained from these OWWEs are easily implemented, producing systems of differential equations at the boundary which are different from those produced by rational approximations, r(s) to √1 - s2. Although these systems are different, a particular choice of difference approximation for the system yields numerical methods such that stability properties of both approaches are equivalent. In particular, for C(s) = 1/r(s), the two systems possess equivalent stability properties. In other cases, numerical results are presented which demonstrate that, where C(s) and r(s) are not derived via interpolation, the C(s) OWWEs can provide better absorption.
KW - Absorbing boundary conditions
KW - Discrete approximations
KW - One-way wave equations
KW - Stability
KW - Well-posedness
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U2 - 10.1016/0377-0427(95)00276-6
DO - 10.1016/0377-0427(95)00276-6
M3 - Article
AN - SCOPUS:0030213509
SN - 0377-0427
VL - 72
SP - 245
EP - 259
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 2
ER -