Abstract
In many fields of application, such as Chemistry or Biology, processes appear which are more naturally modeled by functional differential equations (FDE’s) than by ordinary differential equations (ODE’s). Boundary value problems (BVP’s) for FDE’s appear frequently in the context of optimal control problems.
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
U. Ascher, J. Christiansen, R.D. Russell, “A Collocation Solver for Mixed Order Systems of Boundary Value Problems”, Math. of Comp. vol. 33, 659–679, (1979).
U. Ascher, J. Christiansen, R.D. Russell, “COLSYS A Collocation Code for Boundary Value Problems”, Proc. Conf. for Codes for BVP’s Houston, Texas, 1978.
U. Ascher, R.D. Russell, “Evaluation of B-Splines for Solving Systems of Boundary Value Problems”, Tech. Rep. 77–14, Dept. Computer Sc., University of B.C. Vancouver, Canada.
U. Ascher, R.D. Russell, “Reformulation of Boundary Value Problems into Standard Form”. SIAM Review vol. 23, 238–254 (1981).
G. Bader,“Numerische Behandlung von Randwertproblemen für Funktional-Differentialgleichungen”, University of Heidelberg, Ph.D. Thesis (1984).
H.T. Banks, “Necessary Conditions for Control Problems with variable time Lags”, SIAM J. Control, vol. 1, 9–47, (1968).
H.T. Banks, F. Kappel, “Spline Approximations for Functional Differential Equations”, J. of Diff. Equations, vol. 34, 496–522 (1979).
A. Bellen, “One step Collocation for Delay Differential Equations”, J. of Comp. Appl. Math., vol. 10, (1984).
C. de Boor, B. Swartz, “Collocation at Gaussian Points”, SIAM J. Numer. Anal., vol. 10, 582–606, (1973).
J. Christiansen, R.D. Russell, “Error Analysis for Spline Collocation Methods with Application to Knot Selection” Math. of Comp., vol. 32, 415–419, (1978).
P. Deuflhard, H.-J. Pesch, P. Rentrop, “A Modified Continuation Method for the Numerical Solution of Two-Point Boundary Value problems by Shooting Techniques”, Numer. Math., vol. 26, 327–343, (1976).
M.Q. Jacobs, Ti-Jeun Kao, “An Optimum Settling Problem for Time Lag Systems”, J. of Math. Anal, and Appl., vol. 40, 687–707, (1972).
H.B. Keller, “Accurate Difference Methods for linear ordinary Differential Systems subject to linear Constraints”. SIAM J. Numer. Anal. vol. 6, 8–30, (1969).
K. de Nevers, K. Schmitt, “An Application of the Shooting Method to Boundary Value Problems for Second Order Delay Equations”. J. of Math. Anal. and Appl., vol. 36, 588–597 (1971).
W.H. Ray, M.A. Soliman, “The Optimal Control of Processes containing pure Time Delays-I, Necessary Conditions for an Optimum.” Chem. Engng. Sci., vol. 25, 1911–1925, (1970).
G.W. Reddien, C.C. Travis, “Approximation Methods for Boundary Value Problems of Differential Equations with Functional Arguments”, J. of Math. Analysis and Appl. vol. 46, 62–74, (1974).
R.D. Russell, “Collocation for Systems of Boundary Value Problems”, Num. Math. vol. 23, 119–133, 1974.
R.D. Russell, J. Christiansen, “Adaptive Mesh Selection Strategies for Solving Boundary Value Problems”, SIAM J. Numer. Anal. vol. 15, 59–80, (1978).
M.A. Soliman, W.H. Ray, “Optimal Control of Multivariable Systems with Pure Time Delays”, Automatica vol. 7, 681–689, (1971).
B. Thomas, “Numerische Behandlung von retardierten Differentialgleichungen mit Hilfe der Extrapolationsmethode und Anwendungen auf retardierte Randwertprobleme.” Universität Köln, Diplomarbeit 1973/1974.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Birkhäuser Boston, Inc.
About this chapter
Cite this chapter
Bader, G. (1985). Solving Boundary Value Problems for Functional Differential Equations by Collation. 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_13
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5160-6_13
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-9590-7
Online ISBN: 978-1-4612-5160-6
eBook Packages: Springer Book Archive