Unconditional Instability of Inflow-Dependent Boundary Conditions in Difference Approximations to Hyperbolic Systems.

Abstract

In this paper we study the stability of finite difference approximations to initial-boundary hyperbolic systems. As is well-known, a proper specification of boundary conditions for such systems is essential for their solutions to be well-defined. We prove a discrete analogue of the above - if the numerical boundary conditions are consistent with an inflow part of the problem, they render the overall computation unstable. An example of the inviscid gasdynamics equations is considered. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1981
Accession Number
ADA110481

Entities

People

  • Eitan Tadmor

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Analogs
  • Applied Mathematics
  • Approximation (Mathematics)
  • Boundaries
  • Cauchy Problem
  • Computations
  • Consistency
  • Contracts
  • Difference Equations
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Instability
  • Mathematics
  • Standards
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

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