Time Discretization Techniques

S. Gottlieb, David I. Ketcheson

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Scopus citations

Abstract

The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.
Original languageEnglish (US)
Title of host publicationHandbook of Numerical Analysis
PublisherElsevier BV
Pages549-583
Number of pages35
ISBN (Print)9780444637895
DOIs
StatePublished - Oct 12 2016

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics
  • Numerical Analysis

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