Total Variation Diminishing Runge-Kutta Schemes.

Abstract

In this paper we further explore a class of high order TVD (total variation diminishing) Runge-Kutta time discretization initialized in Shu & Osher (1988), suitable for solving hyperbolic conservation laws with stable spatial discretizations. We illustrate with numerical examples that non-TVD but linearly stable Runge-Kutta time discretization can generate oscillations even for TVD (total variation diminishing) spatial discretization, verifying the claim that TVD Runge-Kutta methods are important for such applications. We then explore the issue of optimal TVD Runge-Kutta methods for second, third and fourth order, and for low storage Runge-Kutta methods.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1996
Accession Number
ADA314231

Entities

People

  • Chi-Wang Shu
  • Sigal Gottlieb

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Coefficients
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  • Euler Equations
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  • Mathematics
  • Oscillation
  • Runge Kutta Method
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Fields of Study

  • Mathematics

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