Solution of Ill-Conditioned linear Two-Point Boundary Value Problems by the Riccati Transformation

Previous article Next article Solution of Ill-Conditioned linear Two-Point Boundary Value Problems by the Riccati TransformationI. H. Mufti, C. K. Chow, and F. T. StockI. H. Mufti, C. K. Chow, and F. T. Stockhttps://doi.org/10.1137/1011096PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] 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[2] G. H. Meyer, On a general theory of characteristics and the method of invariant imbedding, SIAM J. Appl. Math., 16 (1968), 488–509 10.1137/0116039 MR0229443 0155.13302 LinkISIGoogle Scholar[3] R. S. Bucy, Two-point boundary value problems of linear Hamiltonian systems, SIAM J. Appl. Math., 15 (1967), 1385–1389 10.1137/0115121 MR0224894 0155.13104 LinkISIGoogle Scholar[4] R. S. Bucy, Global theory of the Riccati equation, J. Comput. System Sci., 1 (1967), 349–361 MR0229916 0155.14403 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Optimal robot‐environment interaction using inverse differential Riccati equation20 February 2019 | Asian Journal of Control, Vol. 22, No. 4 Cross Ref On the Riccati transfer matrix method for repetitive structuresMechanics Research Communications, Vol. 37, No. 7 Cross Ref Hybrid solution of weakly formulated boundary-value problemsMathematics and Computers in Simulation, Vol. 26, No. 1 Cross Ref A numerical method for linear two-point boundary-value problems using compound matricesJournal of Computational Physics, Vol. 33, No. 1 Cross Ref Asymptotic Series Solution of Singularly Perturbed Fixed-End-Point Problem of Nuclear ReactorJournal of Nuclear Science and Technology, Vol. 15, No. 6 Cross Ref Back-and-forth shooting method for solving two-point boundary-value problemsJournal of Optimization Theory and Applications, Vol. 18, No. 4 Cross Ref A Unified View of Some Methods for Stiff Two-Point Boundary Value ProblemsKarl G. Guderley18 July 2006 | SIAM Review, Vol. 17, No. 3AbstractPDF (2624 KB)A comparison of several invariant imbedding algorithms for the solution of two-point boundary-value problemsApplied Mathematics and Computation, Vol. 1, No. 3 Cross Ref ON THE CONVERSION OF BOUNDARY-VALUE PROBLEMS INTO STABLE INITIAL-VALUE PROBLEMS VIA SEVERAL INVARIANT IMBEDDING ALGORITHMS**Work supported by the U. S. Atomic Energy Commission Cross Ref Suboptimal control of fixed-end-point minimum energy problem via singular perturbation theoryJournal of Mathematical Analysis and Applications, Vol. 45, No. 3 Cross Ref The extended continuation method and invariant imbeddingJournal of Mathematical Analysis and Applications, Vol. 45, No. 1 Cross Ref The numerical solution of elliptic equations by the method of linesComputer Physics Communications, Vol. 4, No. 2 Cross Ref A useful device for certain boundary-value problemsJournal of Computational Physics, Vol. 10, No. 2 Cross Ref Solving Boundary-Value Problems by ImbeddingJournal of the ACM, Vol. 18, No. 4 Cross Ref Volume 11, Issue 4| 1969SIAM Review History Submitted:10 September 1968Published online:18 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1011096Article page range:pp. 616-619ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics