Skip to main content
Log in

Obtaining starting values for the shooting method solution of a class of two-point boundary-value problems

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

A method based on matching a zero of the right-hand side of the differential equations, in a two-point boundary-value problem, to the boundary conditions is suggested. Effectiveness of the procedure is tested on three nonlinear, two-point boundary-value problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Roberts, S. M., andShipman, J. S.,Two-Point Boundary Value Problems: Shooting Methods, American Elsevier Publishing Company, New York, New York, 1972.

    Google Scholar 

  2. Lastman, G. J.,A Modified Newton's Method for Solving Trajectory Optimization Problems, AIAA Journal, Vol. 6, No. 5, 1968.

  3. Lastman, G. J., andTapley, B. D.,Optimization of Non-Linear Systems with Inequality Constraints Explicitly Containing the Control, International Journal of Control, Vol. 12, No. 3, 1970.

  4. Gear, C. W.,Algorithm 407DIFSUB for Solution of Ordinary Differential Equations [D2], Communications of the Association for Computing Machinery, Vol. 14, No. 3, 1971.

  5. Nikolai, P. J.,Certification of Algorithm 407 [D2], Communications of the Association for Computing Machinery, Vol. 16, No. 7, 1973.

  6. Roberts, S. M., andShipman, J. S.,Solution of Troesch's Two-Point Boundary Value Problem by a Combination of Techniques, Journal of Computational Physics, Vol. 10, No. 2, 1972.

  7. Jones, D. J.,Solution of Troesch's, and Other Two-Point Boundary Value Problems by Shooting Methods, Journal of Computational Physics, Vol. 12, No. 3, 1973.

  8. Jacobson, D. H., andMayne, D. Q.,Differential Dynamic Programming, American Elsevier Publishing Company, New York, New York, 1970.

    Google Scholar 

  9. Miele, A., Naqvi, S., Levy, A. V., andIyer, R. R.,Numerical Solution of Nonlinear Equations and Nonlinear Two-Point Boundary-Value Problems, Advances in Control Systems, Vol. 8, Edited by C. T. Leondes, Academic Press, New York, New York, 1972.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by A. Miele

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lastman, G.J. Obtaining starting values for the shooting method solution of a class of two-point boundary-value problems. J Optim Theory Appl 14, 263–270 (1974). https://doi.org/10.1007/BF00932610

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00932610

Key Words

Navigation