Equilibrium states of Runge-Kutta schemes: part II

ABSTRACT

A theory is given that accounts for the observed behavior of Runge-Kutta codes when the stepsize is restricted by stability. The theory deals with the general case when the dominant eigenvalues of the Jacobian may be a complex conjugate pair. This extends and generalizes the results of Part I of this paper, which deal with the real case. Familiarity with Part I is assumed, but not essential.

REFERENCES

• 1: George Hall, Equilibrium states of Runge Kutta schemes, ACM Transactions on Mathematical Software (TOMS), v.11 n.3, p.289-301, Sept. 1985 [doi>10.1145/214408.214424]
• 2: Fred T. Krogh, On Testing a Subroutine for the Numerical Integration of Ordinary Differential Equations, Journal of the ACM (JACM), v.20 n.4, p.545-562, Oct. 1973 [doi>10.1145/321784.321786]
• 3: SHAMPINE, L. F. Stiffness and non-stiff differential equation solvers. In Numerische Behandlung von Differential Gleichungen, L. Collatz, Ed. International Series of Numerical Mathematics, vol. 27. Birkhauser Verlag, Basel, Switzerland, 1975, pp. 287-301.

INDEX TERMS

Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Initial value problems; One-step (single step) methods
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Algorithm design and analysis

General Terms:
Algorithms