Abstract
The boundary locus method for determining the stability region of a linear multistep method is considered from several viewpoints. In particular we show how it is related to the order of the method. These ideas are extended to Runge-Kutta and other methods.
Similar content being viewed by others
References
L. V. Ahlfors,Complex Analysis, McGraw-Hill (1953).
J. C. Butcher,A class of implicit methods for ordinary differential equations, Proceedings of the Dundee Conference on Numerical Analysis (Lecture Notes in Mathematics 506) Springer-Verlag (1975), 28–37.
G. Dahlquist,A special stability problem for linear multistep methods, BIT 3 (1963), 27–43.
J. Dieudonné,Foundations of Modern Analysis, Academic Press (1960).
A. Goetz,Introduction to Differential Geometry, Addison-Wesley (1970).
P. K. Henrici,Discrete Variable Methods in Ordinary Differential Equations, Wiley (1962).
R. Jeltsch,A necessary condition for A-stability of multistep multiderivative methods, Math. Comp. 30 (1976), 739–746.
J. D. Lambert,Computational Methods in Ordinary Differential Equations, Wiley (1973).
W. Liniger,A criterion for A-stability of linear multistep integration formulae, Computing 3 (1968), 280–285.
S. P. Nørsett,A criterion for A(α)-stability of linear multistep methods, BIT 9 (1969), 259–263.
S. P. Nørsett,One-step methods of Hermite type for numerical integration of stiff systems, BIT 14 (1974), 63–77.
J. L. Siemieniuch,Properties of certain rational approximations to e −z, BIT 16 (1976), 172–191.
G. Wanner, E. Hairer and S. P. Nørsett,Order stars and stability theorems, BIT 18 (1978), 475–489.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sanz-Serna, J.M. Some aspects of the boundary locus method. BIT 20, 97–101 (1980). https://doi.org/10.1007/BF01933590
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01933590