Abstract
A continuation method is described for extending the applicability of quasilinearization to numerically unstable two-point boundary-value problems. Since quasilinearization is a realization of Newton's method, one might expect difficulties in finding satisfactory initial trialpoints, which actually are functions over the specified interval that satisfy the boundary conditions. A practical technique for generating suitable initial profiles for quasilinearization is described. Numerical experience with these techniques is reported for two numerically unstable problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bellman, R., andKalaba, R. E.,Quasilinearization and Nonlinear Boundary Value Problems, American Elsevier Publishing Company, New York, 1965.
Goodman, T. R., andLance, G. N.,The Numerical Integration of Two-Point Boundary Value Problems, Mathematical Tables and Other Aids to Computation, Vol. 10, No. 54, 1956.
Roberts, S. M., andShipman, J. S.,Continuation in Shooting Methods for Two-Point Boundary Value Problems, Journal of Mathematical Analysis and Applications, Vol. 18, No. 1, 1967.
Roberts, S. M., andShipman, J. S.,Justification for the Continuation Method in Two-Point Boundary Value Problems, Journal of Mathematical Analysis and Applications (to appear).
Kantorovich, L. V., andAkilov, G. P.,Functional Analysis in Normed Spaces, The Macmillan Company, New York, 1964.
Author information
Authors and Affiliations
Additional information
Communicated by R. E. Kalaba
Rights and permissions
About this article
Cite this article
Roberts, S.M., Shipman, J.S. & Roth, C.V. Continuation in quasilinearization. J Optim Theory Appl 2, 164–178 (1968). https://doi.org/10.1007/BF00926998
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00926998