Two-step runge-kutta methods and hyperbolic partial differential equations

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

The purpose of this study is the design of efficient methods for the solution of an ordinary differential system of equations arising from the semidiscretization of a hyperbolic partial differential equation. Jameson recently introduced the use of one-step Runge-Kutta methods for the numerical solution of the Euler equations. Improvements in efficiency up to 80% may be achieved by using two-step Runge-Kutta methods instead of the classical onestep methods. These two-step Runge-Kutta methods were first introduced by Byrne and Lambert in 1966. They are designed to have the same number of function evaluations as the equivalent one-step schemes, and thus they are potentially more efficient. By solving a nonlinear programming problem, which is specified by stability requirements, optimal two-step schemes are designed. The optimization technique is applicable for stability regions of any shape.

Original languageEnglish (US)
Pages (from-to)563-579
Number of pages17
JournalMathematics of Computation
Volume55
Issue number192
DOIs
StatePublished - 1990

Keywords

  • Hyperbolic partial differential equations
  • Method of lines
  • Pseudo-Runge-Kutta methods
  • Stability

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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