Certain Equivalent Requirements of Approximate Solutions of x' = f (t, x).

Previous article Next article Certain Equivalent Requirements of Approximate Solutions of x' = f (t, x). N. F. StewartN. F. Stewarthttps: //doi. org/10. 1137/0707018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 W. H. Anderson, The solution of simultaneous ordinary differential equations using a general purpose digital computer, Comm. ACM, 3 (1960), 355–360 10. 1145/367297. 367343 MR0127537 0099. 11102 CrossrefISIGoogle Scholar2 J. H. Ash, Masters Thesis, AnAdams Runge-Kutta subroutine for systems of ordinary differential equations, Master's thesis, University of toronto, Ontario, 1965 Google Scholar3 Earl A. Coddington and, Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc. , New York-Toronto-London, 1955xii+429 MR0069338 0064. 33002 Google Scholar4 Germund G. Dahlquist, D. Greenspan, On rigorous error bounds in the numerical solution ofv ordinary differential equationsNumerical Solutions of Nonlinear Differential Equations (Proc. Adv. Sympos. , Madison, Wis. , 1966), John Wiley edited by L. W. Neustadt, Interscience Publishers John Wiley & Sons, Inc. New York-London, 1962viii+360 MR0166037 0102. 32001 Google Scholar24 Emilio Roxin, The existence of optimal controls, Michigan Math. J. , 9 (1962), 109–119 10. 1307/mmj/1028998668 MR0136844 0105. 07801 CrossrefGoogle Scholar25 D. Schermerhorn, KRS3 FORTRAN floating point Runge-Kutta integration, SHARE distribution 3010, Devon, Del. , 1964 Google Scholar26 F. C. Schweppe, Recursive state estimation when observation errors and system inputs are bounded, Sperry Rand Research Center Report, Sudbury, Massachusetts, 1967 Google Scholar27 N. F. Stewart, Masters Thesis, An integration subroutine using a runge-kutta method, master's thesis, university of toronton, ontario, 1965 Google Scholar28 N. F. Stewart, The comparison of numerical methods for ordinary differential equations, Tech. Rep. 3, Department of Computer Science, University of Toronto, Ontario, 1968 Google Scholar29 J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall Inc. , Englewood Cliffs, N. J. , 1963vi+161 MR0161456 1041. 65502 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Runge-Kutta research at TorontoApplied Numerical Mathematics, Vol. 22, No. 1-3 Cross Ref Parallel defect controlBIT, Vol. 31, No. 4 Cross Ref Achieving tolerance proportionality in software for stiff initial-value problemsComputing, Vol. 42, No. 4 Cross Ref Using Interval Methods for the Numerical Solution of ODE'sZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 66, No. 11 Cross Ref Evaluation of implicit formulas for the solution of ODEsBIT, Vol. 19, No. 4 Cross Ref A Theoretical Criterion for Comparing Runge–Kutta FormulasK. R. Jackson, W. H. Enright, and T. E. Hull14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 15, No. 3AbstractPDF (3073 KB) Interval Arithmetic Error-Bounding AlgorithmsL. W. Jackson14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 12, No. 2AbstractPDF (1109 KB) Comparing Numerical Methods for Ordinary Differential EquationsT. E. Hull, W. H. Enright, B. M. Fellen, and A. E. Sedgwick14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 9, No. 4AbstractPDF (3348 KB) Volume 7, Issue 2| 1970SIAM Journal on Numerical Analysis History Submitted: 17 June 1969Published online: 14 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI: 10. 1137/0707018Article page range: pp. 256-270ISSN (print): 0036-1429ISSN (online): 1095-7170Publisher: Society for Industrial and Applied Mathematics