Does error control suppress spuriosity?

SIAM Journal on Numerical Analysis

Volumn 34, Issue 2, 1997, Pages 756-778

  Aves, Mark A ^a   Griffiths, David F ^a   Higham, Desmond J ^a  

^a UNIVERSITY OF DUNDEE   (United Kingdom)

Author keywords

Dynamics; Error control; Long term behavior; Spurious fixed point

Indexed keywords

EID: 0000172812     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994276980     Document Type: Article

References (15)

1. M. A. AVES, D. F. GRIFFITHS, AND D. J. HIGHAM, Does error control suppress spuriosity? Tech. report NA/155, University of Dundee, Dundee, Scotland, 1994.
2. D. P. GRIFFITHS, P. K. SWEBY, AND H. C. YEE, On spurious asymptotic numerical solutions of explicit Runge-Kutta methods, IMA J. Numer. Anal., 12 (1992), pp. 319-338.
3. E. HAIRER, A. ISERLES, AND J. M. SANZ-SERNA, Equilibria of Runge-Kutta methods, Numer. Math., 58 (1990), pp. 243-254.
4. G. HALL, Equilibrium states of Runge-Kutta schemes, ACM Trans. Math, Software, 11 (1985), pp. 289-301.
5. G. HALL AND D. J. HIGHAM, Analysis of stepsize selection schemes for Runge-Kutta codes, IMA J. Numer. Anal., 8 (1988), pp. 305-310.
6. D. J. HIGHAM and A. M. STUART, Analysis of the dynamics of local error control via a piecewise continuous residual, Tech. report SCCM-95-03, Stanford University, Stanford, CA, 1995.
7. A. R. HUMPHRIES, Spurious solutions of numerical methods for initial value problems, IMA J. Numer. Anal., 13 (1993), pp. 263-290.
8. A. ISERLES, Stability and dynamics of numerical methods for nonlinear ordinary differential equations, IMA J. Numer. Anal., 10 (1990), pp. 1-30.
9. A. ISERLES, A. T. PEPLOW, AND A. M. STUART, A unified approach to spurious solutions introduced by time discretisation. Part I: Basic theory, SIAM J. Numer. Anal., 28 (1991), pp. 1723-1751.
10. J. D. LAMBERT, Numerical Methods for Ordinary Differential Systems, John Wiley, New York, 1991.
11. THE MATHWORKS, INC., MATLAB User's Guide, Natick, Massachusetts, 1992.
12. J. M. SANZ-SERNA, Numerical ordinary differential equations vs. dynamical systems, in The Dynamics of Numerics and the Numerics of Dynamics, D.S. Broomhead and A. Iserles, eds., The Institute of Mathematics & Its Applications, Conference Series 34, Oxford University Press, New York, 1992, pp. 81-106.
13. L. F. SHAMPINE AND R. C. ALLEN, Numerical Computing: An Introduction, W. B. Saunders, Philadelphia, PA, 1973.
14. A. M. STUART AND A. R. HUMPHRIES, The essential stability of local error control for dynamical systems, SIAM J. Numer. Anal., 32 (1995), pp. 1940-1971.
15. H. C. YEE, P. K. SWEBY, and D. F. GRIFFITHS, Dynamical systems approach study of spurious steady state numerical solutions of nonlinear differential equations. 1. The ODE connection and its implications for algorithm developments in computational fluid dynamics, J. Comput. Phys., 97 (1991), pp. 249-310.