The Complete Solution of the Fifth Order Runge–Kutta Equations

Previous article Next article The Complete Solution of the Fifth Order Runge–Kutta EquationsC. R. CassityC. R. Cassityhttps://doi.org/10.1137/0706038PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] H. P. Konen and , H. A. Luther, Some singular explicit fifth order Runge-Kutta solutions, SIAM J. Numer. Anal., 4 (1967), 607–619 10.1137/0704055 MR0219239 0159.20504 LinkGoogle Scholar[2] J. C. Butcher, On the attainable order of Runge-Kutta methods, Math. Comp., 19 (1965), 408–417 MR0179943 0132.36401 CrossrefISIGoogle Scholar[3] E. J. Nyström, Über die numerische Integration von Differentialgleichungen, Acta Soc. Sci. Fennicae, 50 (1925), 1–55 Google Scholar[4] H. A. Luther and , H. P. Konen, Some fifth-order classical Runge-Kutta formulas, SIAM Rev., 7 (1965), 551–558 10.1137/1007112 MR0184437 0147.13302 LinkISIGoogle Scholar[5] John Waters, Methods of numerical integration applied to a system having trivial function evaluations, Comm. ACM, 9 (1966), 293–296 10.1145/365278.365553 0143.37702 CrossrefISIGoogle Scholar[6] J. Douglas Lawson, An order five Runge-Kutta process with extended region of stability, SIAM J. Numer. Anal., 3 (1966), 593–597 10.1137/0703051 MR0216760 0154.40602 LinkGoogle Scholar[7] W. Kutta, Beitrag zur näherungsweisen Integration totaler Differentialgleichungen, Z. Math. Physik, 46 (1901), 435–452 Google Scholar[8] C. R. Cassity, Solutions of the fifth-order Runge-Kutta equations, SIAM J. Numer. Anal., 3 (1966), 598–606 10.1137/0703052 MR0216756 0154.40603 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Runge–Kutta pairs of orders 8(7) with extended stability regions for addressing linear inhomogeneous systemsMathematical Methods in the Applied Sciences, Vol. 6 | 27 September 2022 Cross Ref Runge–Kutta Embedded Methods of Orders 8(7) for Use in Quadruple Precision ComputationsMathematics, Vol. 10, No. 18 | 7 September 2022 Cross Ref Explicit Runge–Kutta pairs with lower stage-orderNumerical Algorithms, Vol. 65, No. 3 | 16 November 2013 Cross Ref HIGH ORDER EMBEDDED RUNGE-KUTTA SCHEME FOR ADAPTIVE STEP-SIZE CONTROL IN THE INTERACTION PICTURE METHODJournal of the Korea Society for Industrial and Applied Mathematics, Vol. 17, No. 4 | 25 Dec 2013 Cross Ref A family of fifth-order Runge-Kutta pairsMathematics of Computation, Vol. 65, No. 215 | 1 January 1996 Cross Ref A General Family of Explicit Runge–Kutta Pairs of Orders $6(5)$S. N. Papakostas, Ch. Tsitouras, and G. PapageorgiouSIAM Journal on Numerical Analysis, Vol. 33, No. 3 | 1 August 2006AbstractPDF (2226 KB)On deriving explicit Runge-Kutta methodsConference on Applications of Numerical Analysis | 27 August 2006 Cross Ref On one-step methods utilizing the second derivativeHiroshima Mathematical Journal, Vol. 1, No. 2 | 1 Jan 1971 Cross Ref Volume 6, Issue 3| 1969SIAM Journal on Numerical Analysis317-522 History Submitted:15 January 1968Published online:14 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0706038Article page range:pp. 432-436ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics