A Finite-Difference Solution to a Mixed-Type Partial Differential Equation: An Ocean Dynamic Motion Model

Abstract

A mixed-type (hyperbolic, parabolic, elliptic) partial differential equation, which results from a model of a towed cylindrical acousitc antenna in the ocean, has been resolved by combining the techniques of the method of lines and the numerical ordingary differential equation method. The model describes the transverse dynamic motion of a zero bending rigidity cylinder in an axial viscous stream. This initially ill-posed problem was satisfactorily solved by the above approach. The efficiency of this numerical solution has been improved over previous solutions. Discussions of these improvements are the main theme of this paper which presents an explicit finite-difference scheme; the improvements increase computation speed while maintaining the required accuracy. The improvements are discussed both theoretically and computationally with respect to consistency, stability and convergence. The results of a numerical test example are given in this reprints.

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Document Details

Document Type
Technical Report
Publication Date
May 31, 1988
Accession Number
ADA227769

Entities

People

  • Ding Lee
  • Robert M. Kennedy

Organizations

  • Naval Underwater Systems Center

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Axial Flow
  • Bessel Functions
  • Boundaries
  • Computations
  • Consistency
  • Convergence
  • Deflection
  • Difference Equations
  • Differential Equations
  • Equations
  • Equations Of Motion
  • Excitation
  • Flow
  • Fluid Flow
  • Partial Differential Equations
  • Stability Conditions

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Structural Dynamics.