Valková, Anna On total truncation error estimation for the one-step method. (English) Zbl 0628.65049 Apl. Mat. 32, 177-185 (1987). The author describes a method for the estimation of the global error of a certain fifth order Runge-Kutta method for the numerical solution of a system of ordinary differential equations. Reviewer: G.Merz MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems Keywords:global error estimation; fifth order Runge-Kutta method; system × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] E. Bukovics: Beiträge zur numerischen Integration II. Monatshefte für Math., Bd 57 (1953), 333-350. · Zbl 0051.35004 · doi:10.1007/BF01503071 [2] B. A. Galler D. P. Rozenberg: Generalization of a Theorem of Carr on Error Bounds for Runge-Kutta Procedures. J. Assoc. Comput. Mach. 7 (I960), 57-60. · Zbl 0096.10101 · doi:10.1145/321008.321015 [3] A. Hu\?a: Contribution to the numerical solution of differential equations by means of Runge-Kutta Formulas with Newton-Cotes numbers weights. Acta Facultatis R. N. Univ. Comen. - Mathematica XXVIII (1972), 51-65. · Zbl 0262.65042 [4] V. Jukl: Fehlerabschätzung der Nyström’schen Formel. Acta Facult. R.N. Univ. Comen. - Mathematica XXIV (1970), 81-100. · Zbl 0216.48902 [5] Max. Lotkin: On accuracy of Runge-Kutta’s Method. Math. Tabl. Oth. Aids. Comp. 5 (1951) 128-133. · Zbl 0044.33104 · doi:10.2307/2002436 [6] E. J. Nyström: Über die numerische Integration von Differentialgleichungen. Acta Soc. Sci. Fennicae, Tom 50, nr. 13, 1-55 (1925). · JFM 51.0427.01 [7] A. Ralston: A first course in numerical analysis. (1965) by McGraw-Hill, Inc. New York. · Zbl 0139.31603 [8] A. Valková: A theoretical formula for an error of the Hu\?a formula of the Runge-Kutta type of the fifth order. Acta Mathematica Universitatis Comenianae XL-XLI (1982), 111-128. [9] A. Valková: A local error estimation of the formulas of the Runge-Kutta-Hu\?a type of the fifth and sixth order. Acta Mathematica Universitatis Comenianae XLII-XLIII (1983). · Zbl 0536.65059 [10] O. Vejvoda: Error estimation for the Runge-Kutta formula. (Czech). Apl. mat. 2 (1957), 1-23. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.