Relative Stability in the Numerical Solution of Ordinary Differential Equations

Previous article Next article Relative Stability in the Numerical Solution of Ordinary Differential EquationsAnthony RalstonAnthony Ralstonhttps://doi.org/10.1137/1007011PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] P. E. Chase, Stability properties of predictor-corrector methods for ordinary differential equations, J. Assoc. Comput. Mach., 9 (1962), 457–468 MR0163436 (29:738) 0106.10502 CrossrefISIGoogle Scholar[2] Germund G. Dahlquist, Stability questions for some numerical methods for ordinary differential equationsProc. Sympos. Appl. Math., Vol. XV, Amer. Math. Soc., Providence, R.I., 1963, 147–158, Experimental Arithmetic, High Speed Computing and Mathematics MR0161475 (28:4679) 0123.32405 CrossrefGoogle Scholar[3] George Emanuel, The Wilf stability criterion for numerical integration, J. Assoc. Comput. Mach., 10 (1963), 557–561 MR0166919 (29:4192) 0234.65022 CrossrefISIGoogle Scholar[4] R. W. Hamming, Stable predictor-corrector methods for ordinary differential equations., J. Assoc. Comput. Mach., 6 (1959), 37–47 MR0102179 (21:973) 0086.11201 CrossrefISIGoogle Scholar[5] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons Inc., New York, 1962xi+407 MR0135729 (24:B1772) 0112.34901 Google Scholar[6] T. E. Hull and , A. C. R. Newbery, Corrector formulas for multi-step integration methods, J. Soc. Indust. Appl. Math., 10 (1962), 351–369 10.1137/0110026 MR0152150 (27:2130) 0108.12702 LinkISIGoogle Scholar[7] T. E. Hull and , A. C. R. Newbery, Integration procedures which minimize propagated errors, J. Soc. Indust. Appl. Math., 9 (1961), 31–47 10.1137/0109004 MR0120770 (22:11519) 0107.10802 LinkISIGoogle Scholar[8] D. H. Lehmer, A machine method for solving polynomial equations, J. Assoc. Comput. Mach., 2 (1961), 151–162 CrossrefGoogle Scholar[9] William Edmund Milne, Numerical solution of differential equations, John Wiley & Sons Inc., New York, 1953xii+275 MR0068321 (16,864c) Google Scholar[10] A. Ralston, A symmetric matrix formulation of the Hurwitz-Routh stability criterion, IRE Trans. on Automatic Control, 7 (1962), 50–51 10.1109/TAC.1962.1105474 CrossrefISIGoogle Scholar[11] A. Ralston, Some theoretical and computational matters relating to predictor-corrector methods of numerical integration, Comput. J., 4 (1961), 64–67 10.1093/comjnl/4.1.64 CrossrefISIGoogle Scholar[12] Herbert S. Wilf, A stability criterion for numerical integration, J. Assoc. Comput. Mach., 6 (1959), 363–365 MR0107370 (21:6095) CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails REFERENCES Cross Ref Adams-type methods with increased ranges of stabilityComputers & Mathematics with Applications, Vol. 4, No. 4 Cross Ref Corrector methods with increased ranges of stabilityComputers & Mathematics with Applications, Vol. 3, No. 3 Cross Ref Stability of multistep methods for delay differential equationsMathematics of Computation, Vol. 30, No. 134 Cross Ref A User-Oriented Program for Crash Dynamics1 February 1974 Cross Ref Liapunov functions for non-linear difference equation stability analysis†International Journal of Control, Vol. 15, No. 5 Cross Ref Predictor-Corrector Algorithms with Identical Regions of StabilityJ. D. Lambert14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 8, No. 2AbstractPDF (713 KB)4 Predictor-Corrector Methods Cross Ref Variable mesh multistep methods for ordinary differential equationsJournal of Computational Physics, Vol. 5, No. 2 Cross Ref Linear multistep methods with mildly varying coefficients1 January 1970 | Mathematics of Computation, Vol. 24, No. 109 Cross Ref Block implicit one-step methods1 January 1969 | Mathematics of Computation, Vol. 23, No. 108 Cross Ref Stabilitätsbereiche bei Diskretisierungsverfahren für Systeme Gewöhnlicher Differentialgleichungen Cross Ref A note on the effect of conditionally stable correctors1 January 1967 | Mathematics of Computation, Vol. 21, No. 100 Cross Ref Predictor-Corrector Methods of High Order With Improved Stability CharacteristicsJournal of the ACM, Vol. 13, No. 3 Cross Ref A Study of Strong and Weak Stability in Discretization AlgorithmsHans J. Stetter14 July 2006 | Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, Vol. 2, No. 2AbstractPDF (1365 KB) Volume 7, Issue 1| 1965SIAM Review History Submitted:13 July 1964Published online:01 August 2006 InformationCopyright © 1965 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1007011Article page range:pp. 114-125ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics