Boundary Value Problems for Ordinary Differential Equations

Abstract

Previous article Next article Boundary Value Problems for Ordinary Differential EquationsL. F. ShampineL. F. Shampinehttps://doi.org/10.1137/0705019PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. Picard, Sur l'application des méthodes d'approximations successives à l'étude de certaines équations différentielles ordinaires, J. Math., 9 (1893), 217–271 25.0507.02 Google Scholar[2] F. Lettenmeyer, Über die von einem Punkt ausgehenden Integralkurven einer Differentialgleichung zweiter Ordnung, Deutsche Math., 7 (1942), 56–74 MR0017830 (8,205i) 0027.21902 Google Scholar[3] P. Ciarlet, Masters Thesis, Variational methods for non-linear boundary-value problems, Doctoral thesis, Case Institute of Technology, Cleveland, Ohio, 1966 Google Scholar[4] Milton Lees, Discrete methods for nonlinear two-point boundary value problemsNumerical Solution of Partial Differential Equations (Proc. Sympos. Univ. 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Vol. V, Interscience Publishers, Inc., New York, 1957viii+238 MR0094665 (20:1177) 0078.09404 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A symbolic algorithm for solving linear two-point boundary value problems by modified Picard techniqueMathematical and Computer Modelling, Vol. 49, No. 1-2 | 1 Jan 2009 Cross Ref A high order B-spline collocation method for linear boundary value problemsApplied Mathematics and Computation, Vol. 191, No. 1 | 1 Aug 2007 Cross Ref On the convergence of finite difference methods for a class of two-point boundary value problems with periodic boundary conditionsApplied Mathematics and Computation, Vol. 75, No. 2-3 | 1 Mar 1996 Cross Ref High order discrete method for a class of two-point boundary value problems with periodic boundary conditionsMathematical and Computer Modelling, Vol. 21, No. 8 | 1 Apr 1995 Cross Ref On the stability of a classical second order method for solving a class of two-point boundary value problemsApplied Mathematics and Computation, Vol. 59, No. 2-3 | 1 Dec 1993 Cross Ref ReferencesOperator Inequalities | 1 Jan 1980 Cross Ref Newton's method for nonlinear ordinary and partial differential equationsJournal of Mathematical Analysis and Applications, Vol. 70, No. 2 | 1 Aug 1979 Cross Ref On the Convergence of the Finite Difference Method for Nonlinear Ordinary Boundary Value ProblemsConstructive Methods for Nonlinear Boundary Value Problems and Nonlinear Oscillations | 1 Jan 1979 Cross Ref Das Parallelenverfahren für Operatorgleichungen und Seine Anwendung auf Nichtlineare RandwertaufgabenNumerische Behandlung von Differentialgleichungen Band 2 | 1 Jan 1976 Cross Ref NUMERICAL SOLUTION OF BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS: SURVEY AND SOME RECENT RESULTS ON DIFFERENCE METHODSNumerical Solutions of Boundary Value Problems for Ordinary Differential Equations | 1 Jan 1975 Cross Ref Solution of a nonlinear two point boundary value problemNumerische Mathematik, Vol. 23, No. 1 | 1 Feb 1974 Cross Ref Use of Fast Direct Methods for the Efficient Numerical Solution of Nonseparable Elliptic EquationsPaul Concus and Gene H. GolubSIAM Journal on Numerical Analysis, Vol. 10, No. 6 | 14 July 2006AbstractPDF (1976 KB)A collocation method for boundary value problemsNumerische Mathematik, Vol. 19, No. 1 | 1 Feb 1972 Cross Ref Einschließungssätze für periodische Lösungen der Liénardschen DifferentialgleichungComputing, Vol. 5, No. 3 | 1 Sep 1970 Cross Ref Boundary Value Problems for Ordinary Differential Equations. II: Patch Bases and Monotone MethodsL. F. ShampineSIAM Journal on Numerical Analysis, Vol. 6, No. 3 | 14 July 2006AbstractPDF (1531 KB)Invariant imbedding and the calculation of eigenvalues for Sturm-Liouville systemsComputing, Vol. 4, No. 1 | 1 March 1969 Cross Ref Error bounds and variational methods for nonlinear boundary value problemsNumerische Mathematik, Vol. 12, No. 5 | 1 Dec 1968 Cross Ref Volume 5, Issue 2| 1968SIAM Journal on Numerical Analysis199-459 History Submitted:12 July 1967Published online:03 August 2006 InformationCopyright © 1968 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0705019Article page range:pp. 219-242ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics