Difference schemes for the parabolic wave equation in ocean acoustics

Tony F. Chan; Longjun Shen; Ding Lee

doi:10.1016/0898-1221(85)90169-5

Difference schemes for the parabolic wave equation in ocean acoustics

Tony F. Chan^*, Longjun Shen, Ding Lee

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We introduce and analyze a collection of difference schemes for the numerical solution of a model multidimensional equation of Schrödinger type with applications to the three-dimensional parabolic wave equation arising from the sound propagation in the ocean. This collection of methods includes explicit and implicit schemes, two-level and three-level schemes and real and complex schemes. Many of these are analogous to classical schemes for the heat equation and the wave equation, but some schemes are unique to the Schrödinger equation. Von Neumann type stability results are given for all schemes. Numerical results arising from the application to an ocean acoustic problem are presented.

Original language	English (US)
Pages (from-to)	747-754
Number of pages	8
Journal	Computers and Mathematics with Applications
Volume	11
Issue number	7-8
DOIs	https://doi.org/10.1016/0898-1221(85)90169-5
State	Published - 1985
Externally published	Yes

Bibliographical note

Funding Information:
Acknowledgements--This work was supported in part by Department of Energy Grant DE-ACO2-81ER 10996, by Army Research Office Grant DAAG-83-0177. by Office of Naval Research Grant N00014-82-K-0184, and by Naval Underwater Systems Center Independent Research Project A65020.

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/0898-1221(85)90169-5

Cite this

@article{be96a5a1e7274961af2b401af0419f4a,

title = "Difference schemes for the parabolic wave equation in ocean acoustics",

abstract = "We introduce and analyze a collection of difference schemes for the numerical solution of a model multidimensional equation of Schr{\"o}dinger type with applications to the three-dimensional parabolic wave equation arising from the sound propagation in the ocean. This collection of methods includes explicit and implicit schemes, two-level and three-level schemes and real and complex schemes. Many of these are analogous to classical schemes for the heat equation and the wave equation, but some schemes are unique to the Schr{\"o}dinger equation. Von Neumann type stability results are given for all schemes. Numerical results arising from the application to an ocean acoustic problem are presented.",

author = "Chan, {Tony F.} and Longjun Shen and Ding Lee",

note = "Funding Information: Acknowledgements--This work was supported in part by Department of Energy Grant DE-ACO2-81ER 10996, by Army Research Office Grant DAAG-83-0177. by Office of Naval Research Grant N00014-82-K-0184, and by Naval Underwater Systems Center Independent Research Project A65020.",

year = "1985",

doi = "10.1016/0898-1221(85)90169-5",

language = "English (US)",

volume = "11",

pages = "747--754",

journal = "Computers and Mathematics with Applications",

issn = "0898-1221",

publisher = "Elsevier",

number = "7-8",

}

TY - JOUR

T1 - Difference schemes for the parabolic wave equation in ocean acoustics

AU - Chan, Tony F.

AU - Shen, Longjun

AU - Lee, Ding

N1 - Funding Information: Acknowledgements--This work was supported in part by Department of Energy Grant DE-ACO2-81ER 10996, by Army Research Office Grant DAAG-83-0177. by Office of Naval Research Grant N00014-82-K-0184, and by Naval Underwater Systems Center Independent Research Project A65020.

PY - 1985

Y1 - 1985

N2 - We introduce and analyze a collection of difference schemes for the numerical solution of a model multidimensional equation of Schrödinger type with applications to the three-dimensional parabolic wave equation arising from the sound propagation in the ocean. This collection of methods includes explicit and implicit schemes, two-level and three-level schemes and real and complex schemes. Many of these are analogous to classical schemes for the heat equation and the wave equation, but some schemes are unique to the Schrödinger equation. Von Neumann type stability results are given for all schemes. Numerical results arising from the application to an ocean acoustic problem are presented.

AB - We introduce and analyze a collection of difference schemes for the numerical solution of a model multidimensional equation of Schrödinger type with applications to the three-dimensional parabolic wave equation arising from the sound propagation in the ocean. This collection of methods includes explicit and implicit schemes, two-level and three-level schemes and real and complex schemes. Many of these are analogous to classical schemes for the heat equation and the wave equation, but some schemes are unique to the Schrödinger equation. Von Neumann type stability results are given for all schemes. Numerical results arising from the application to an ocean acoustic problem are presented.

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U2 - 10.1016/0898-1221(85)90169-5

DO - 10.1016/0898-1221(85)90169-5

M3 - Article

AN - SCOPUS:0021467561

SN - 0898-1221

VL - 11

SP - 747

EP - 754

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 7-8

ER -

Difference schemes for the parabolic wave equation in ocean acoustics

Abstract

Bibliographical note

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