Previous |  Up |  Next


global error estimation; fifth order Runge-Kutta method; system; differential equations; numerical solution; fifth order; error analysis
In this paper the author establishes estimation of the total truncation error after $s$ steps in the fifth order Ruge-Kutta-Huťa formula for systems of differential equations. The approach is analogous to that used by Vejvoda for the estimation of the classical formulas of the Runge-Kutta type of the 4-th order.
[1] E. Bukovics: Beiträge zur numerischen Integration II. Monatshefte für Math., Bd 57 (1953), 333-350. DOI 10.1007/BF01503071 | MR 0059629 | Zbl 0051.35004
[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. MR 0145673
[3] A. Huťa: 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. MR 0309313
[4] V. Jukl: Fehlerabschätzung der Nyström'schen Formel. Acta Facult. R.N. Univ. Comen. - Mathematica XXIV (1970), 81-100. MR 0305601 | Zbl 0216.48902
[5] Max. Lotkin: On accuracy of Runge-Kutta's Method. Math. Tabl. Oth. Aids. Соmр. 5 (1951) 128-133. MR 0043566
[6] E. J. Nyström: Über die numerische Integration von Differentialgleichungen. Acta Soc. Sci. Fennicae, Тоm 50, nr. 13, 1-55 (1925).
[7] A. Ralston: A first course in numerical analysis. (1965) by McGraw-Hill, Inc. New York. MR 0191070 | Zbl 0139.31603
[8] A. Valková: A theoretical formula for an error of the Huťa formula of the Runge-Kutta type of the fifth order. Acta Mathematica Universitatis Comenianae XL-XLI (1982), 111-128. MR 0686967
[9] A. Valková: A local error estimation of the formulas of the Runge-Kutta-Huťa type of the fifth and sixth order. Acta Mathematica Universitatis Comenianae XLII-XLIII (1983).
[10] O. Vejvoda: Error estimation for the Runge-Kutta formula. (Czech). Apl. mat. 2 (1957), 1-23.
Partner of
EuDML logo