A Perturbation Technique for Nonlinear Two-Point Boundary Value Problems

Previous article Next article A Perturbation Technique for Nonlinear Two-Point Boundary Value ProblemsS. M. Roberts, J. S. Shipman, and W. J. EllisS. M. Roberts, J. S. Shipman, and W. J. Ellishttps://doi.org/10.1137/0706032PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Richard Bellman, Perturbation techniques in mathematics, physics, and engineering, Holt, Rinehart and Winston, Inc., New York, 1964viii+118 MR0161003 Google Scholar[2] Richard E. Bellman and , Robert E. Kalaba, Quasilinearization and nonlinear boundary-value problems, Modern Analytic and Computional Methods in Science and Mathematics, Vol. 3, American Elsevier Publishing Co., Inc., New York, 1965ix+206 MR0178571 0139.10702 Google Scholar[3] F. A. Ficken, The continuation method for functional equations, Comm. Pure Appl. Math., 4 (1951), 435–456 MR0045308 0043.32202 CrossrefISIGoogle Scholar[4] T. R. Goodman and , G. N. Lance, The numerical integration of two-point boundary value problems, Math. Tables Aids Comput., 10 (1956), 82–86 MR0081553 0071.34006 CrossrefGoogle Scholar[5] L. V. Kantorovich and , G. P. Akilov, Functional analysis in normed spaces, Translated from the Russian by D. E. Brown. Edited by A. P. Robertson. International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Co., New York, 1964xiii+771 MR0213845 0127.06104 Google Scholar[6] S. M. Roberts and , J. S. Shipman, The Kantorovich theorem and two-point boundary value problems, IBM J. Res. Develop., 10 (1966), 402–406 MR0202325 0196.49704 CrossrefISIGoogle Scholar[7] S. M. Roberts and , J. S. Shipman, Continuation in shooting methods for two-point boundary value problems, J. Math. Anal. Appl., 18 (1967), 45–58 10.1016/0022-247X(67)90181-3 MR0207213 0155.47303 CrossrefISIGoogle Scholar[8] S. M. Roberts, , J. S. Shipman and , C. V. Roth, Continuation in quasilinearization, J. 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ACM, 7 (1964), 366–373 10.1145/512274.512291 MR0168123 0123.11805 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Survey of time-optimal attitude maneuversJournal of Guidance, Control, and Dynamics, Vol. 17, No. 2 Cross Ref An Asymptotic Perturbation Method for Nonlinear Optimal Control Problems Cross Ref Role of continuation in engineering analysisChemical Engineering Science, Vol. 42, No. 6 Cross Ref Numerical solution of nonlinear equations by one-parameter imbedding methods26 June 2007 | Numerical Functional Analysis and Optimization, Vol. 3, No. 2 Cross Ref Solution of nonlinear boundary value problems—XIChemical Engineering Science, Vol. 34, No. 5 Cross Ref One-parameter imbedding techniques for the solution of nonlinear boundary-value problemsApplied Mathematics and Computation, Vol. 4, No. 4 Cross Ref A classification and survey of numerical methods for boundary value problems in ordinary differential equationsInternational Journal for Numerical Methods in Engineering, Vol. 11, No. 5 Cross Ref NUMERICAL SOLUTION OF BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS: SURVEY AND SOME RECENT RESULTS ON DIFFERENCE METHODS Cross Ref BOUNDARY PROBLEM SOLVERS FOR FIRST ORDER SYSTEMS BASED ON DEFERRED CORRECTIONS Cross Ref Variable order variable step finite difference methods for nonlinear boundary value problems28 August 2006 Cross Ref A variable order finite difference method for nonlinear multipoint boundary value problems1 January 1974 | Mathematics of Computation, Vol. 28, No. 128 Cross Ref Extension of a perturbation technique for nonlinear two-point boundary-value problems3 August 2013 | Journal of Optimization Theory and Applications, Vol. 12, No. 5 Cross Ref The epsilon variation method in two-point boundary-value problems3 August 2013 | Journal of Optimization Theory and Applications, Vol. 12, No. 2 Cross Ref Numerical Solutions by the Continuation MethodE. Wasserstrom18 July 2006 | SIAM Review, Vol. 15, No. 1AbstractPDF (2435 KB)Solution of Troesch's two-point boundary value problem by a combination of techniquesJournal of Computational Physics, Vol. 10, No. 2 Cross Ref A survey of optimal structural design under dynamic constraintsInternational Journal for Numerical Methods in Engineering, Vol. 4, No. 4 Cross Ref Solving Boundary-Value Problems by ImbeddingJournal of the ACM, Vol. 18, No. 4 Cross Ref Volume 6, Issue 3| 1969SIAM Journal on Numerical Analysis History Submitted:27 February 1968Published online:14 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0706032Article page range:pp. 347-358ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics