Boundary-Dependent Stability Criteria for Difference Approximations of Hyperbolic Problems. I.

Abstract

One-step, explicit, dissipative approximations to scalar hyperbolic problems are studied in the quarter plane x > or = 0, t > or = 0. In both, outflow and inflow cases, Kreiss' theory is used to derive sufficient stability criteria which are independent of the basic difference scheme, and are stated entirely in terms of the boundary conditions. These criteria take a very simple form when the boundary conditions are translatory. The results are applied to several well-known boundary treatments, and overall stability is achieved without effort.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1977
Accession Number
ADA049501

Entities

People

  • Eitan Tadmor
  • Moshe Goldberg

Organizations

  • University of California, Los Angeles

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Amplification
  • Boundaries
  • California
  • Cauchy Problem
  • Classification
  • Coefficients
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Mathematics
  • Polynomials
  • Scalar Functions
  • Scientific Research
  • Universities

Fields of Study

  • Mathematics

Readers

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