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

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13 Scopus citations


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
Issue number192
StatePublished - 1990


  • 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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