Previous article Next article Integration Procedures Which Minimize Propagated ErrorsT. E. Hull and A. C. R. NewberyT. E. Hull and A. C. R. Newberyhttps://doi.org/10.1137/0109004PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Germund Dahlquist, Convergence and stability in the numerical integration of ordinary differential equations, Math. Scand., 4 (1956), 33–53 MR0080998 0071.11803 CrossrefGoogle Scholar[2] Germund Dahlquist, Stability and error bounds in the numerical integration of ordinary differential equations, Inaugural dissertation, University of Stockholm, Almqvist & Wiksells Boktryckeri AB, Uppsala, 1958, 87– MR0100966 0085.33401 Google Scholar[3] R. W. Hamming, Stable predictor-corrector methods for ordinary differential equations. , J. Assoc. Comput. Mach., 6 (1959), 37–47 MR0102179 0086.11201 CrossrefISIGoogle Scholar[4] F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1956x+511 MR0075670 0070.12401 Google Scholar[5] T. E. Hull and , W. A. J. Luxemburg, Numerical methods and existence theorems for ordinary differential equations, Numer. Math., 2 (1960), 30–41 10.1007/BF01386206 MR0114017 0089.29003 CrossrefGoogle Scholar[6] T. E. Hull and , A. C. R. Newbery, Error bounds for a family of three-point integration procedures, J. Soc. Indust. Appl. Math., 7 (1959), 402–412 10.1137/0107033 MR0136079 0094.31005 LinkISIGoogle Scholar[7] Zdeněk Kopal, Operational methods in numerical analysis based on rational approximations, On numerical approximation. Proceedings of a Symposium, Madison, April 21-23, 1958, Edited by R. E. Langer. Publication no. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin, The University of Wisconsin Press, Madison, 1959, 25–43 MR0102165 0084.11402 Google Scholar[8] C. Lanczos, Selected topics in applied analysis, Lecture notes, Department of Mathematics, Oregon State College, Corvallis, 1957–58, part II Google Scholar[9] W. E. Milne and , R. R. Reynolds, Stability of a numerical solution of differential equations, J. Assoc. Comput. Mach., 6 (1959), 196–203 MR0102182 0091.12102 CrossrefISIGoogle Scholar[10] W. E. Milne and , R. R. Reynolds, Stability of a numerical solution of differential equations. II, J. Assoc. Comput. Mach., 7 (1960), 46–56 MR0145668 0097.33101 CrossrefISIGoogle Scholar[11] W. Quade, Numerische Integration von gewöhnlichen Differentialgleichungen durch Interpolation nach Hermite, Z. Angew. Math. Mech., 37 (1957), 161–169 MR0088058 0077.32504 CrossrefGoogle Scholar[12] Heinz Rutishauser, Über die Instabilität von Methoden zur Integration gewöhnlicher Differentialgleichungen, Z. Angew. Math. Physik, 3 (1952), 65–74 10.1007/BF02080985 MR0046146 0046.13303 CrossrefGoogle Scholar[13] Herbert E. Salzer, Osculatory extrapolation and a new method for the numerical integration of differential equations, J. Franklin Inst., 262 (1956), 111–119 10.1016/0016-0032(56)90758-X MR0081550 CrossrefGoogle Scholar[14] Herbert E. Salzer, Numerical integration of $y''=\phi(x,y,y')$ using osculatory interpolation, J. Franklin Inst., 263 (1957), 401–409 10.1016/0016-0032(57)90279-X MR0085608 0168.13906 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Comparing Numerical Methods for Ordinary Differential EquationsSIAM Journal on Numerical Analysis, Vol. 9, No. 4 | 14 July 2006AbstractPDF (3348 KB)A Search for Optimum Methods for the Numerical Integration of Ordinary Differential EquationsSIAM Review, Vol. 9, No. 4 | 18 July 2006AbstractPDF (1114 KB)Relative Stability in the Numerical Solution of Ordinary Differential EquationsSIAM Review, Vol. 7, No. 1 | 1 August 2006AbstractPDF (1131 KB)Corrector Formulas for Multi-Step Integration MethodsT. E. Hull and A. C. R. NewberyJournal of the Society for Industrial and Applied Mathematics, Vol. 10, No. 2 | 13 July 2006AbstractPDF (2082 KB) Volume 9, Issue 1| 1961Journal of the Society for Industrial and Applied Mathematics1-164 History Submitted:06 June 1960Published online:10 July 2006 InformationCopyright © 1961 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0109004Article page range:pp. 31-47ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics