Optimal runge-kutta methods for first order pseudospectral operators

J. L. Mead, Rosemary Renaut

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


New Runge-Kutta methods for method of lines solution of systems of ordinary differential equations arising from discretizations of spatial derivatives in hyperbolic equations, by Chebyshev or modified Chebyshev methods, are introduced. These Runge-Kutta methods optimize the time step necessary for stable solutions, while holding dispersion and dissipation fixed. It is found that maximizing dispersion minimizes dissipation, and vice versa. Optimal methods with respect to large stability intervals on the imaginary axis and with respect to the eigenvalue spectra of the underlying pseudospectral discretizations are developed. In the latter case, stability regions are optimized to include the outliers of the spatial operators. Performance on a model problem in computational aeroacoustics is evaluated. The optimized schemes have two more function evaluations per timestep than the standard fourth order Runge-Kutta method, but allow timesteps up to 1.7 times larger. Moreover, dissipation and dispersion are reduced.

Original languageEnglish (US)
Pages (from-to)404-419
Number of pages16
JournalJournal of Computational Physics
Issue number1
StatePublished - Jun 10 1999


  • Computational aeroacoustics
  • Dispersion
  • Dissipation
  • Hyperbolic equations
  • Pseudospectral Chebyshev
  • Runge-Kutta

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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