Abstract
This paper examines shooting and multiple shooting as a technique for the analysis of numerical schemes applied to two point boundary value problems. The aim of the analysis is to deduce convergence of a numerical scheme by establishing the convergence of the scheme when applied to a number of subproblems. Since such an approach is useful only if the subproblems are reasonably well conditioned, the question of conditioning is addressed. It is shown that there exist subproblems that are at least as well conditioned as the original problem. Two examples are presented for which the shooting approach leads to a substantial simplification in the analysis.
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
Ascher, U. and Weiss, R. Collocation for singular perturbation problems II: Linear first order systems without turning points. Math. Comp 43 (1984), 157–187.
de Boor, C., de Hoog, F. and de Keller, H. The stability of one step schemes for first-order two-point boundary value problems, SIAM J. Numer. Anal., 20 (1983), 1139–1146.
de Hoog, F. and Mattheij, R., On dichotomy and well conditioning in boundary value problems, submitted for publication.
Keller, H.B., Numerical solution of two-point boundary value problems, SIAM regional conference series, 24, Philadelphia, 1976.
Lentini, L., Osborne, M.R. and Russell, R.D., The close relationships between methods for solving two-point boundary value problems, to appear in SINUM.
Weiss, R., An analysis of the box and trapezoidal schemes for linear singularly perturbed boundary value problems, Math. Comp 42 (1984), 41–67.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Birkhäuser Boston, Inc.
About this chapter
Cite this chapter
de Hoog, F., Mattheij, R. (1985). The Role of Conditioning in Shooting Techniques. 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_2
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5160-6_2
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-9590-7
Online ISBN: 978-1-4612-5160-6
eBook Packages: Springer Book Archive