Matches in SemOpenAlex for { <https://semopenalex.org/work/W2055969714> ?p ?o ?g. }
Showing items 1 to 55 of
55
with 100 items per page.
- W2055969714 abstract "In 1926 Prufer introduced a method of transforming the second order Sturm‐Liouville (SL) equation into two nonlinear first order differential equations for the phase o/ and “magnitude”, |o/2+o/2| for a Poincare phase space representation, (o/,o/). The useful property is the phase equation decouples from the magnitude one which leads to a nonlinear, two point boundary value problem for the eigenvalues, or SL numbers. The transformation has been used both theoretically, e.g. Atkinson, [1960] to prove certain properties of SL equations as well as numerically e.g Bailey [1978]. This paper examines the utility of the Prufer transformation in the context of numerical solutions for modes of the ocean acoustic wave equation. (Its use is certainly not well known in the ocean acoustics community.) Equations for the phase, o/, and natural logarithm of the “magnitude”, ln(|o/2+o/2|) lead to same decoupling and a fast and efficient numerical solution with the SL eigenvalues mapping to the horizontal wavenubers. The Prufer transformation has stabilty problems for low order modes at high frequecies, so a numerically stable method of integrating the phase equation is derived. This seems to be the first time the these stability issues have been highlighted to provide a robust algorthim for the modes." @default.
- W2055969714 created "2016-06-24" @default.
- W2055969714 creator A5004690387 @default.
- W2055969714 creator A5024931347 @default.
- W2055969714 creator A5039040352 @default.
- W2055969714 creator A5039404411 @default.
- W2055969714 creator A5059577719 @default.
- W2055969714 date "2010-01-01" @default.
- W2055969714 modified "2023-09-26" @default.
- W2055969714 title "Prufer Transformations for the Normal Modes in Ocean Acoustics" @default.
- W2055969714 cites W1493744842 @default.
- W2055969714 cites W1568666422 @default.
- W2055969714 cites W1627801536 @default.
- W2055969714 cites W1972354568 @default.
- W2055969714 cites W1978899628 @default.
- W2055969714 cites W2007657616 @default.
- W2055969714 cites W2021631998 @default.
- W2055969714 cites W2025233220 @default.
- W2055969714 cites W2062910337 @default.
- W2055969714 cites W2079160640 @default.
- W2055969714 doi "https://doi.org/10.1063/1.3493087" @default.
- W2055969714 hasPublicationYear "2010" @default.
- W2055969714 type Work @default.
- W2055969714 sameAs 2055969714 @default.
- W2055969714 citedByCount "2" @default.
- W2055969714 countsByYear W20559697142022 @default.
- W2055969714 crossrefType "proceedings-article" @default.
- W2055969714 hasAuthorship W2055969714A5004690387 @default.
- W2055969714 hasAuthorship W2055969714A5024931347 @default.
- W2055969714 hasAuthorship W2055969714A5039040352 @default.
- W2055969714 hasAuthorship W2055969714A5039404411 @default.
- W2055969714 hasAuthorship W2055969714A5059577719 @default.
- W2055969714 hasConcept C121332964 @default.
- W2055969714 hasConcept C24890656 @default.
- W2055969714 hasConcept C41008148 @default.
- W2055969714 hasConceptScore W2055969714C121332964 @default.
- W2055969714 hasConceptScore W2055969714C24890656 @default.
- W2055969714 hasConceptScore W2055969714C41008148 @default.
- W2055969714 hasLocation W20559697141 @default.
- W2055969714 hasOpenAccess W2055969714 @default.
- W2055969714 hasPrimaryLocation W20559697141 @default.
- W2055969714 hasRelatedWork W2096946506 @default.
- W2055969714 hasRelatedWork W2130043461 @default.
- W2055969714 hasRelatedWork W2350741829 @default.
- W2055969714 hasRelatedWork W2358668433 @default.
- W2055969714 hasRelatedWork W2376932109 @default.
- W2055969714 hasRelatedWork W2382290278 @default.
- W2055969714 hasRelatedWork W2390279801 @default.
- W2055969714 hasRelatedWork W2748952813 @default.
- W2055969714 hasRelatedWork W2899084033 @default.
- W2055969714 hasRelatedWork W3004735627 @default.
- W2055969714 isParatext "false" @default.
- W2055969714 isRetracted "false" @default.
- W2055969714 magId "2055969714" @default.
- W2055969714 workType "article" @default.