George Hall
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.
- 1 HALL, G. Equilibrium states of Runge-Kutta schemes. A CM Trans. Math. Softw. 11, 3 (Sept. 1985), 289-301. Google Scholar
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- 2 KROGH, F.T. On testing a subroutine for the numerical integration of ordinary differential equations. J. ACM 20, 4 (Oct. 1973), 545-562. Google ScholarDigital Library
- 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.Google Scholar
Index Terms
- Equilibrium states of Runge-Kutta schemes: part II
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Reviews
Michael Minkoff
This paper deals with the behavior of Runge-Kutta methods when stepsize is restricted by stability requirements. In Part I (see ACM Trans. Math Softw. 11, 3 (Sept. 1985), 289–301), this requirement was studied in the case when the dominant eigenvalue of the Jacobian is real. In the current paper, this analysis is extended to the complex case, thus completing the theory. The paper presents the theory within the context of a model problem and provides numerical examples as well.
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