Initial-Boundary Value Problems for Hyperbolic Equations and Their Difference Approximation with Characteristic Boundary.

Abstract

This work consists of two parts. In the first, we consider initial-boundary value problems for strictly hyperbolic systems with constant coefficients: By using the technique of lambda-matrix, we obtain an a priori estimate, which assures the continuous dependence of the solution on the inhomogeneous terms of the equations. This work generalizes the former results of Majda and Osher (1975) also to the nonsymmetrical case, simplifies their proofs an removes some of their assumptions. In Part II, we develop stability theory for Burstein difference scheme approximating the above problem(m=2) with additional assumption det (A ALPHA +B2B)=0. Particularly, the problem of constructing the Kreiss symmetrizer for general multidimensional dissipative approximations is resolved, thus removing the only obstacle in developing stability theory for such approximations in the noncharacteristic case.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1980
Accession Number
ADA097010

Entities

People

  • Daniel Michelson

Organizations

  • Tel Aviv University

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Air Force
  • Analytic Functions
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Complex Variables
  • Construction
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Ions
  • Scientific Research
  • Theorems
  • Two Dimensional
  • United States

Fields of Study

  • Mathematics

Readers

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