Integration Procedures Which Minimize Propagated Errors

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 SectionsAbout1 Germund Dahlquist, Convergence and stability in the numerical integration of ordinary differential equations, Math. Scand. , 4 (1956), 33–53 MR0080998 0071. 11803 CrossrefGoogle Scholar2 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 Scholar3 R. W. Hamming, Stable predictor-corrector methods for ordinary differential equations. , J. Assoc. Comput. Mach. , 6 (1959), 37–47 MR0102179 0086. 11201 CrossrefISIGoogle Scholar4 F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Company, Inc. , New York-Toronto-London, 1956x+511 MR0075670 0070. 12401 Google Scholar5 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 Scholar6 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 Scholar7 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 Scholar8 C. Lanczos, Selected topics in applied analysis, Lecture notes, Department of Mathematics, Oregon State College, Corvallis, 1957–58, part II Google Scholar9 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 Scholar10 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 Scholar11 W. Quade, Numerische Integration von gewöhnlichen Differentialgleichungen durch Interpolation nach Hermite, Z. Angew. Math. Mech. , 37 (1957), 161–169 MR0088058 0077. 32504 CrossrefGoogle Scholar12 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 Scholar13 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 Scholar14 Herbert E. Salzer, Numerical integration of y''= (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