Strong Stability Preserving High-order Time Discretization Methods

Abstract

In this paper we review and further develop a class of strong-stability preserving (SSP) high-order time discretizations for semi-discrete method-of-lines approximations of partial differential equations. Termed TVD (total variation diminishing) time discretizations before this class of high-order time discretization methods preserves the strong-stability properties of first-order Euler time stepping and has proved very useful especially in solving hyperbolic partial differential equations. The new contributions in this paper include the development of optimal explicit SSP linear Runge-Kutta methods, their application to the strong stability of coercive approximations, a systematic study of explicit SSP multi-step methods, and a study of the strong-stability preserving property of implicit Runge-Kutta and multi-step methods.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 2000
Accession Number
ADA376446

Entities

People

  • Chi-Wang Shu
  • Eitan Tadmor
  • Sigal Gottlieb

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Applied Mathematics
  • Coefficients
  • Computers
  • Differential Equations
  • Electronic Mail
  • Equations
  • High Resolution
  • Inequalities
  • Intervals
  • Mathematics
  • Numbers
  • Partial Differential Equations
  • Real Numbers
  • Rhode Island
  • Runge Kutta Method
  • Wave Equations

Fields of Study

  • Mathematics

Readers

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