Higher Order Accuracy Finite Difference Algorithms for Quasi-Linear, Conservation-Law Hyperbolic Systems,

Abstract

An explicit algorithm that yields finite difference equations that approximate the quasi-linear hyperbolic system to any desired accuracy, for an arbitrary number of space dimensions, is presented. Analytic stability proofs and criteria, in the case of one dimension for arbitrary order of accuracy, are given. Analytic stability proofs in the higher order dimensional cases, up to and including 3rd order accuracy with sufficient stability conditions, are shown. Numerical examples are compared with analytic solutions and demonstrate that the indicated accuracy was achieved. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1972
Accession Number
AD0753097

Entities

People

  • D. Gottlieb
  • S. Abarbanel

Organizations

  • Tel Aviv University

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Difference Equations
  • Differential Equations
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Real Variables
  • Stability Conditions

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space