Higher-order parabolic approximations to time-independent wave equations
- 1 September 1983
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 24 (9) , 2301-2304
- https://doi.org/10.1063/1.525978
Abstract
A sequence of numerically tractable higher-order parabolic approximations is derived for the reduced wave equation in an inhomogeneous medium. The derivation is motivated by a definition of waves propagating in a distinguished direction. For a homogeneous medium these definitions are exact and yield uncoupled, infinite-order parabolic equations which are equivalent to the wave equation. The difficulty of obtaining higher-order parabolic approximations for the elastic wave equation in an inhomogeneous medium is also discussed.Keywords
This publication has 3 references indexed in Scilit:
- Parabolic approximations to the time-independent elastic wave equationJournal of Mathematical Physics, 1982
- Generalizations of the Bremmer series based on physical conceptsJournal of Mathematical Analysis and Applications, 1969
- The W.K.B. approximation as the first term of a geometric‐optical seriesCommunications on Pure and Applied Mathematics, 1951