Abstract
In this paper various issues related to the development of effective software for second order initial value problems are discussed. In particular the difficulty caused by high frequency negligible components is identified and a class of multistep formulas suitable for problems with these components is proposed. The difficulties involved in choosing an appropriate error control strategy are reviewed and a particular strategy is proposed and justified.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C.A. Addison (1980), Numerical methods for a class of second order ODEs arising in structural dynamics, Ph.D. Thesis, appeared as Dept. Comp. Sc. Tech. Rep. No. 147/80, University of Toronto, Toronto.
C.A. Addison and W.H. Enright (1981), Properties of multistep formulas intended for a class of second order ODES, submitted to SIAM J. Number. Anal.
D.G. Bettis and M.K. Horn (1978), Embedded Runge-Kutta-Nystrom algorithms of order two through six, TICOM Rep. No. 78-3, University of Texas, Austin.
A.C. Hindmarsh (1980), LSODE and LSODEI, two new initial value ordinary differential equation solvers, ACM SIGNUM Newsletter, 15, pp. 10–12.
T.E. Hull, W.H. Enright and K.R. Jackson (1976), Users guide for DVERK-a subroutine for solving non-stiff IODEs, Dept. of Comp. Sc. Tech. Rep. No. 100, University of Toronto, Toronto.
F.T. Krogh (1971), Suggestion on conversion (with listings) of the variable order integrators VODQ, SVDA and DVDQ, J.P.L. Tech. Memo. 278, Jet Propulsion Laboratory, CIT, Pasadena.
F.T. Krogh (1975), Summary of test results with variants of a variable order Adams method, Computing Memo. 376, Section 914, Jet Propulsion Laboratory, CIT, Pasadena.
L.F. Shampine and M.K. Gordon (1975), Computer Solution of Ordinary Differential Equations, W.H. Freeman, San Francisco.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
Enright, W.H. (1982). Developing effective multistep methods for the numerical solution of systems of second order initial value problems. In: Hennart, J.P. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092970
Download citation
DOI: https://doi.org/10.1007/BFb0092970
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11193-1
Online ISBN: 978-3-540-38986-6
eBook Packages: Springer Book Archive