Abstract
The code TOM, for the solution of boundary value problems, is based on linear multistep methods used as BVMs [5, 6, 16, 17]. Among the peculiar features of this code, the mesh selection strategy, based on two measures of conditioning of the problem, seems the most interesting. In this paper the application of the code to the classical Holt problem, one of the most famous and difficult BVP, will permit to stress the effectiveness of such approach along with the utility of the additional information provided by the two measures.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R.P. Agarwal and R.C. Gupta, On the solution of the Holt’s problem. BIT 24 (1984), 342–346.
U. Ascher, J. Christiansen, and R.D. Russell, Colsys — a collocation code for boundary value problems. Lecture Notes Comp. Sc. (B. Childs et al., ed.), vol. 76, Springer Verlag, 1979, pp. 164–185.
U. Ascher, R. Mattheij, and R.D. Russell, Numerical solution of boundary value problems for odes. Prentice-Hall, Englewood CliffsNJ, 1988.
K. Balla and M. Vicsek, On the reduction of Holt’s problem to a finite interval. Numer. Math. 51 (1987), 291–302.
L. Brugnano and D. Trigiante, A new mesh selection strategy for odes. Appl. Numer. Math. 24 (1997), 1–21.
Solving differential problems by multistep initial and boundary value methods. Gordon & Breach, Amsterdam, 1998.
J. Cash, G. Moore, and R. Wright, An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems. ACM Transaction of Mathematical Software 27 (2001), no. 2, 245–266.
J.R. Cash and M.H. Wright, A deferred correction method for nonlinear two-point boundary value problems: implementation and numerical evaluation. SIAM J. Sci. Statist. Comput. 12 (1991), no. 4, 971–989.
E.J. Dean, An inexact Newton method for nonlinear two-point boundary value problems. J. Optim. Theory Appl. 75 (1992), no. 3, 471–486.
W.H. Enright and P.H. Muir, Runge-Kutta software with defect control for boundary value odes. SIAM J. Sci. Comput. 17 (1996), 479–497.
J.F. Holt, Numerical solution of nonlinear two-point boundary problems by finite difference methods. Comm. ACM 7 (1964), 366–373.
D.J. Jones, Solution of Troesch’s, and other, two-point boundary problems by shooting techniques. J. Comput. Phys. 12 (1973), 429–434.
J. Kierzenka and L.F. Shampine, A BVP solver based on residual control and the MATLAB pse. ACM Transaction of Mathematical Software 27 (2001), no. 3, 299–316.
W.S. King and W.S. Lewellen, Boundary-layer similarity solutions for rotating flows with and without magnetic interaction. Phys. Fluids 7 (1964), 1674–1680.
N. Labianca, F. Mazzia, and D. Trigiante, Soluzione numerica di problemi ai valori al contorno: applicazione al modello differenziale del rendez-vous. CAPI2002–6° Workshop sul Calcolo ad Alte Prestazioni in Italia http://www.cilea.it/convegni/CAPI2002/index.htm.
F. Mazzia and I. Sgura, Numerical approximation of nonlinear bops by means of bums. Appl. Numer. Math. 42 (2002), no. 1–3, 337–352.
F. Mazzia and D. Trigiante, Mesh selection strategy for Boundary Value Problems (to be published on Numerical Algorithms).
A. Miele, A.K. Agarwal, and J.L. Tietze, Solution of two-point boundary-value problems with Jacobian matrix characterized by large positive eigenvalues. J. Comput. Phys. 15 (1974), 117–133.
M.R. Osborne, On shooting methods for boundary value problems. J. Math. Anal. Appl. 27 (1969), 417–433.
S.M. Roberts and J.S. Shipman, Multipoint solution of two-point boundary-value problems. J. Optim. Theory Applic. 7 (1971), 301–318.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Basel AG
About this paper
Cite this paper
Aceto, L., Mazzia, F., Trigiante, D. (2003). The Performances of the Code TOM on the Holt Problem. In: Antreich, K., Bulirsch, R., Gilg, A., Rentrop, P. (eds) Modeling, Simulation, and Optimization of Integrated Circuits. ISNM International Series of Numerical Mathematics, vol 146. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8065-7_22
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8065-7_22
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9426-5
Online ISBN: 978-3-0348-8065-7
eBook Packages: Springer Book Archive