Comparing routines for the numerical solution of initial value problems of ordinary differential equations in multiple shooting

Aziz, A. K. (ed.): Numerical solutions of boundary value problems for ordinary differential equations. Proceedings of a Symposium held at the University of Maryland, 1974. New York: Academic Press 1975 Bauer, H., Neumann, K.: Berechnung optimaler Steuerungen, Maximumprinzip und dynamische Optimierung. Lecture Notes in Operations Research and Mathematical Systems, Vol. 17. Berlin-Heidelberg-New York: Springer 1969 Broyden, C. G.: A class of methods for solving non-linear simultaneous equations. Math. Comp.19, 577–593 (1965) Bulirsch, R.: Numerical calculation of elliptic integrals and elliptic functions, I, II. Numer. Math.7, 78–90, 353-354 (1965) Bulirsch, R., Oettli, W., Stoer, J. (eds.): Optimization and optimal control. Proceedings of a Conference held at Oberwolfach, 1974, Lecture Notes, Vol. 477. Berlin-Heidelberg-New York: Springer 1975 Bulirsch, R., Stoer, J.: Numerical treatment of ordinary differential equations by extrapolation methods. Numer. Math.8, 1–13 (1966) Bulirsch, R., Stoer, J., Deuflhard, P.: Numerical solution of nonlinear two-point boundary value problems, I. Numer. Math. (to be published) Cole, J. D., Keller, H. B., Saffmann, P. G.: The flow a viscous compressible fluid through a very narrow gap. SIAM J. Appl. Math.15, 605–617 (1967) Daniel, J. W., Martin, A. J.: Implementing deferred corrections for Numerov's difference method for second-order two-point boundary value problems. Tech. Rep. CNA-107, Center for Numerical Analysis, The University of Texas at Austin (1975) Davenport, S. M., Shampine, L. F., Watts, H. A.: Comparison of some codes for the initial value problem for ordinary differential equations. In: [1], pp. 349–353 (1975) Deuflhard, P.: A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting. Numer. Math.22, 289–315 (1974) Deuflhard, P.: A relaxation strategy for the modified Newton method. In [5], pp. 59–73 1975 Deuflhard, P., Pesch, H.-J., Rentrop, P.: A modified continuation method for the numerical solution of nonlinear two-point boundary value problems by shooting techniques. Numer. Math.26, 327–343 (1976) Dickmanns, E. D.: Maximum range, three-dimensional lifting planetary entry. NASA Tech. Rep. R-M 199, Marshall Space Flight Center, Alabama (1972) Dickmanns, E. D., Pesch, H.-J.: Influence of a reradiative heating constraint on lifting entry trajectories for maximum lateral range. 11th International Symposium on Space Technology and Science, Tokyo, July 1975 Enright, W. H., Bedet, R., Farkas, I., Hull, T. E.: Test results on initial value methods for non-stiff ordinary differential equations. Tech. Rep. No. 68, Department of Computer Science, University of Toronto (1974) England, R.: Error estimates for Runge-Kutta type solutions to systems of ordinary differential equations. Comp. J.12, 166–170 (1969) Fehlberg, E.: Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweitenkontrolle. Computing4, 93–106 (1969) Fehlberg, E.: Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweitenkontrolle und ihre Anwendung auf Wärmeleitungsprobleme. Computing6, 61–71 (1970) Fermi, E., Pasta, J. R., Ulam, S.: Studies of nonlinear problems, I. Tech. Rep. No. 1940, Los Alamos (1955) Gragg, W. B.: On extrapolation algorithms for ordinary initial value problems. SIAM J. Numer. Anal. Ser. B2, 384–403 (1965) Holt, J. F.: Numerical solution of nonlinear two-point boundary value problems by finite difference methods. Comm. ACM.7, 366–373 (1964) Hull, T. E.: Numerical solutions of initial value problems for ordinary differential equations. In: [1], pp. 3–26 (1975) Hussels, H. G.: Schrittweitensteuerung bei der Integration gewöhnlicher Differentialgleichungen mit Extrapolationsverfahren. Universität zu Köln, Mathemathisches Institut, Diplomarbeit (1973) Keller, H. B.: Numerical methods for two-point boundary value problems. Chapter 6: Practical examples and computational exercises. London: Blaisdell 1968 King, W. S., Lewellen, W. S.: Boundary-layer similarity solutions for rotating flows with and without magnetic interaction. Ref. ATN-63 (9227)-6, Aerodynamics and Propulsion Res. Lab., Aerospace Corp., El Segundo. Calif. (1963) Küpper, T.: A singular bifurcation problem. Math. Rep. No. 99, Battelle Advanced Studies Center, Geneva (1976) Lentini, M., Pereyra, V.: Boundary problem solvers for first order systems based on deferred corrections. In: [1], pp. 293–315 (1975) Na, T. Y., Tang, S. C.: A method for the solution of conduction heat transfer with non-linear heat generation. ZAMM49, 45–52 (1969) Pereyra, V.: High order finite difference solution of differential equations. Report STAN-CS-73-348, Computer Science Department, Stanford University (1973) Pesch, H.-J.: Numerische Berechnung optimaler Steuerungen mit Hilfe der Mehrzielmethode dokumentiert am Problem der Rückführung eines Raumgleiters unter Berücksichtigung von Aufheizungsbegrenzungen. Universität zu Köln, Mathematisches Institut, Diplomarbeit (1973) Pimbley, G.: Eigenfunction branches of nonlinear operators and their bifurcations. Lecture Notes, Vol. 104. Berlin-Heidelberg-New York: Springer 1969 Reissner, E., Weinitschke, H. J.: Finite pure bending of circular cylindrical tubes. Quarterly Appl. Math.20, 305–319 (1963) Rentrop, P.: Numerical solution of the singular Ginzburg-Landau equations by multiple shooting. Computing16, 61–67 (1976) Roberts, S. M., Shipman, J. S.: Two-point boundary value problems: Shooting methods. New York: Elsevier 1972 Russel, R. D., Shampine, L. F.: A collocation method for boundary value problems. Numer. Math.19, 1–28 (1972) Scott, M. R.: Invariant imbedding and its applications to ordinary differential equations: An introduction. Reading, Massachusetts: Addison-Wesley 1973 Scott, M. R., Watts, H. A.: SUPORT—A computer code for two-point boundary-value problems via orthonormalization. Tech. Rep. SAND-75-0198. Sandia Laboratories, Albuquerque, New Mexico (1975) Sedgwick, A. E.: An effective variable order variable step Adams method. Ph. D. Thesis, Tech. Rep. No. 53, Department of Computer Science, University of Toronto (1973) Stoer, J., Bulirsch, R.: Einführung in die Numerische Mathematik, 11. Heidelberger Taschenbuch, Bd. 114. Berlin-Heidelberg-New York: Springer 1973 Stoleru, L. G.: An optimal policy for economic growth. Econometrica33, 321–348 (1965) Thurston, G. A.: Newton's method applied to problems in nonlinear mechanics. J. Appl. Mech.32, 383–388 (1965) Weinitschke, H. J.: Die Stabilität elliptischer Zylinderschalen bei reiner Biegung. ZAMM50, 411–422 (1970) Weinitschke, H. J.: On nonsymmetric bending instability of elliptic cylindrical tubes. Unpublished manuscript, TU Berlin (to appear) Wick, R.: Numerische Lösung volkswirtschaftlicher Variationsprobleme mit Zustandsbeschränkungen unter Anwendung der Mehrzielmethode. Universität zu Köln, Mathematisches Institut, Diplomarbeit (1973)