A stable explicit scheme for the ocean acoustic wave equation

Tony F. Chan*, Longjun Shen, Ding Lee

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A class of ocean acoustic wave propagation problems is represented by a parabolic equation of the Schrodinger type. Using conventional explicit finite difference schemes, e.g. the Euler scheme, to solve the parabolic wave equation is unstable. Thus, important advantages of explicit schemes are completely missing. This paper presents a conditionally stable explicit scheme by introducing an extra dissipative term. This new explicit scheme is then applied to solve the ocean acoustic parabolic wave equation fully utilizing the advantages of explicit schemes. The theoretical development, the computational aspects, and the advantages are discussed. Application of the scheme to a realistic ocean acoustic problem is included. The solution obtained is compared with the unconditionally stable Crank-Nicolson solution.

Original languageEnglish (US)
Pages (from-to)929-936
Number of pages8
JournalComputers and Mathematics with Applications
Issue number9
StatePublished - Sep 1985
Externally publishedYes

Bibliographical note

Funding Information:
A~~~~~o~r~/ed,cr,t~f~ra.ut-hTohres would like to thank Professor Martin H. Schultr of Yale University for his many valuable discuwons as well as his encouragement to apply the scheme for real applications. This work was supported m part by the Department of Energy under contract DE-ACOZ-8lERl0996. by Army Research Office under contract DAAG-83-0177. by Office of Naval Research Grant N00014-82-K-0184. and by Naval Underwater Systems Center Independent Research Protect A65020.

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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