Numerical Methods Based on Additive Splittings for Hyperbolic Partial Differential Equations,

Abstract

We derive and analyze several methods for systems of hyperbolic equations with wide ranges of signal speeds. These techniques are also useful for problems whose coefficients have large mean values about which they oscillate with small amplitude. Our methods are based on additive splittings of the operators into components that can be approximated independently on the different time scales, some of which are sometimes treated exactly. The efficiency of the splitting methods is seen to depend on the error incurred in splitting the exact solution operator. This is analyzed and a technique is discussed for reducing this error through a simple change of variables. A procedure for generating the appropriate boundary data for the intermediate solutions is also presented. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1981
Accession Number
ADA110530

Entities

People

  • Joseph Oliger
  • Randall J. LeVeque

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Additives (Chemicals)
  • Boundary Value Problems
  • Cauchy Problem
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Computers
  • Differential Equations
  • Equations
  • Errors
  • Linear Accelerators
  • Method Of Characteristics
  • Navier Stokes Equations
  • Numerical Analysis
  • Partial Differential Equations
  • Theorems

Fields of Study

  • Mathematics

Readers

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