Construction of two-step Runge-Kutta methods of high order for ordinary differential equations

Z. Bartoszewski, Zdzislaw Jackiewicz

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

The construction of two-step Runge-Kutta methods of order p and stage order q = p with stability polynomial given in advance is described. This polynomial is chosen to have a large interval of absolute stability for explicit methods and to be A-stable and L-stable for implicit methods. After satisfying the order and stage order conditions the remaining free parameters are computed by minimizing the sum of squares of the difference between the stability function of the method and a given polynomial at a sufficiently large number of points in the complex plane.

Original languageEnglish (US)
Pages (from-to)51-70
Number of pages20
JournalNumerical Algorithms
Volume18
Issue number1
DOIs
StatePublished - 1998

Keywords

  • Least squares minimization
  • Stability analysis
  • Two-step Runge-Kutta methods

ASJC Scopus subject areas

  • Applied Mathematics

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