Abstract
Shooting methods for nonlinear boundary value problems are examined. It is shown that the methods converge whenever the problem is well posed in the sense that the solution to be computed is isolated.
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References
E. A. Coddington and N. Levinson,Theory of Ordinary Differential Equations, International Series in Pure and Applied Mathematics, New York, McGraw-Hill, 1955.
E. Isaacson and H. B. Keller,Analysis of Numerical Methods, New York. John Wiley and Sons, Inc., 1966.
L. S. Jennings and M. R. Osborne,Applications of orthogonal matrix transformations to the solution of systems of linear and nonlinear equations, Technical Report No. 37, Computer Centre, The Australian National University, Canberra, A.C.T. 2600.
H. B. Keller,Numerical Methods for Two Point Boundary Value Problems, London. Blaisdell, 1968.
H. B. Keller,Accurate difference methods for linear ordinary differential systems subject to linear constraints, SIAM J. Num. Anal 6 (1969), 8–30.
H. B. Keller,Approximation methods for nonlinear problems, manuscript.
J. Kowalik and M. R. Osborne,Methods for Unconstrained Optimization Problems, New York. American Elsevier Publ. Comp. Inc., 1968.
M. R. Osborne,On shooting methods for boundary value problems, J. Math. Anal. Appl. 27 (1969), 417–433.
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Weiss, R. The convergence of shooting methods. BIT 13, 470–475 (1973). https://doi.org/10.1007/BF01933411
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DOI: https://doi.org/10.1007/BF01933411