| Title:
|
On total truncation error estimation for the one-step method (English) |
| Author:
|
Valková, Anna |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1987 |
| Pages:
|
177-185 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Slovak |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
global error estimation |
| Keyword:
|
fifth order Runge-Kutta method |
| Keyword:
|
system |
| Keyword:
|
differential equations |
| Keyword:
|
numerical solution |
| Keyword:
|
fifth order |
| Keyword:
|
error analysis |
| MSC:
|
34A34 |
| MSC:
|
65G99 |
| MSC:
|
65L05 |
| idZBL:
|
Zbl 0628.65049 |
| idMR:
|
MR0895876 |
| DOI:
|
10.21136/AM.1987.104249 |
| . |
| Date available:
|
2008-05-20T18:32:12Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104249 |
| . |
| Reference:
|
[1] E. Bukovics: Beiträge zur numerischen Integration II.Monatshefte für Math., Bd 57 (1953), 333-350. Zbl 0051.35004, MR 0059629, 10.1007/BF01503071 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[4] V. Jukl: Fehlerabschätzung der Nyström'schen Formel.Acta Facult. R.N. Univ. Comen. - Mathematica XXIV (1970), 81-100. Zbl 0216.48902, MR 0305601 |
| Reference:
|
[5] Max. Lotkin: On accuracy of Runge-Kutta's Method.Math. Tabl. Oth. Aids. Соmр. 5 (1951) 128-133. MR 0043566 |
| Reference:
|
[6] E. J. Nyström: Über die numerische Integration von Differentialgleichungen.Acta Soc. Sci. Fennicae, Тоm 50, nr. 13, 1-55 (1925). |
| Reference:
|
[7] A. Ralston: A first course in numerical analysis.(1965) by McGraw-Hill, Inc. New York. Zbl 0139.31603, MR 0191070 |
| Reference:
|
[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 |
| Reference:
|
[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). |
| Reference:
|
[10] O. Vejvoda: Error estimation for the Runge-Kutta formula.(Czech). Apl. mat. 2 (1957), 1-23. |
| . |
