Abstract
The standard method of multiple shooting for a system of n first order differential equations, with k unknown initial conditions requires the integration of k sets of variational equations on the first shot, and n sets of variational equations on every shot thereafter. This paper describes a variant of multiple shooting that requires the solution of k sets of variational equations on every shot. The technique applies to both linear and nonlinear boundary value problems. Techniques to deal with difficulties unique to the solution of nonlinear problems are suggested.
This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics & Space Administration.
This is a preview of subscription content, log in via an institution to check access.
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
David D. Morrison, James D. Riley, and John F. Zancanaro, “Multiple shooting method for two-point boundary value problems”, Comm. ACM 5 (1962), pp. 613–614.
Herbert B. Keller, Numerical Methods for Two-Point Boundary Value Problems, Ginn-Blaisdell, Waltham, Mass. 1968.
Herbert B. Keller, Numerical Solution of Two-Point Boundary Value Problems, Regional Conference Series in Applied Mathematics, No. 24, Society for Industrial and Applied Mathematics, Philadelphia, Pa. 1976.
Michael R. Osborne, “On the Numerical Solution of Boundary Value Problems for Ordinary Differential Equations”, Information Processing ’74, North Holland, Amsterdam, 1974, pp. 673–677.
Peter Deuflhard, “Recent advances in multiple shooting techniques”, in Computational techniques for ordinary differential equations, Academic Press, New York, 1980, pp. 217–272.
John H. George and Robert W. Gunderson, “Conditioning of linear boundary value problems”, BIT 12, (1972), pp. 172–181.
Marianela Lentini, Michael R. Osborne and Robert D. Russell, “The close relationships between methods for solving two-point boundary value problems”, to appear in SIAM J. Numer. Anal.
S.D. Conte, “The numerical solution of boundary value problems”, SIAM Rev. 8 (1966), pp. 309–321.
M.R. Scott and H.A. Watts, “Computational solution of linear two point boundary value problems via orthonormalization”, SIAM J. Numer. Anal. 14, (1977), pp. 40–70.
Michael R. Osborne, “The stabilized march is stable”, SIAM J. Numer. Anal. 16, (1979), pp. 923–933.
R.M.M. Mattheij and G.W.M. Staarink, “An efficient algorithm for solving general linear two point BVP”, Report 8220, Math. Inst. Catholic University, Nijmegen, (1982).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Birkhäuser Boston, Inc.
About this chapter
Cite this chapter
Krogh, F.T., Keener, J.P., Enright, W.H. (1985). Reducing the Number of Variational Equations in the Implementation of Multiple Shooting. In: Ascher, U.M., Russell, R.D. (eds) Numerical Boundary Value ODEs. Progress in Scientific Computing, vol 5. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5160-6_7
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5160-6_7
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-9590-7
Online ISBN: 978-1-4612-5160-6
eBook Packages: Springer Book Archive