| Title:
|
Order conditions for partitioned Runge-Kutta methods (English) |
| Author:
|
Jackiewicz, Zdzisław |
| Author:
|
Vermiglio, Rossana |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
301-316 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We illustrate the use of the recent approach by P. Albrecht to the derivation of order conditions for partitioned Runge-Kutta methods for ordinary differential equations. (English) |
| Keyword:
|
partitioned Runge-Kutta method |
| Keyword:
|
ordinary differential equation |
| Keyword:
|
order conditions |
| MSC:
|
65L05 |
| MSC:
|
65L06 |
| idZBL:
|
Zbl 1058.65069 |
| idMR:
|
MR1763174 |
| DOI:
|
10.1023/A:1022323529349 |
| . |
| Date available:
|
2009-09-22T18:04:05Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134441 |
| . |
| Reference:
|
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| Reference:
|
[2] P. Albrecht: A new theoretical approach to Runge-Kutta methods.SIAM J. Numer. Anal. 24 (1987), 391–406. Zbl 0617.65067, MR 0881373, 10.1137/0724030 |
| Reference:
|
[3] P. Albrecht: The Runge-Kutta theory in a nutshell.SIAM J. Numer. Anal. 33 (1996), 1712–1735. Zbl 0858.65074, MR 1411846, 10.1137/S0036142994260872 |
| Reference:
|
[4] H. Brunner, E. Hairer and S. P. Nørsett: Runge-Kutta theory for Volterra integral equations of the second kind.Math. Comp. 39 (1982), 147–163. MR 0658219, 10.1090/S0025-5718-1982-0658219-8 |
| Reference:
|
[5] E. Griepentrog: Gemischte Runge-Kutta-Verfahren für steife Systeme.In: Seminarbericht Nr. 11, Sekt, Math., Humboldt Univ. Berlin, 1978, pp. 19–29. Zbl 0434.65044, MR 0540731 |
| Reference:
|
[6] E. Hairer: Order conditions for numerical methods for partitioned ordinary differential equations.Numer. Math. 36 (1981), 431–445. Zbl 0462.65049, MR 0614858, 10.1007/BF01395956 |
| Reference:
|
[7] E. Hairer, S. P. Nørsett and G. Wanner: Solving Ordinary Differential Equations I. Nonstiff Problems.Springer-Verlag, Berlin-Heidelberg-New York, 1991. MR 1227985 |
| Reference:
|
[8] Z. Jackiewicz, R. Vermiglio: General linear methods with external stages of different orders.BIT 36 (1996), 688–712. MR 1420272, 10.1007/BF01733788 |
| Reference:
|
[9] Z. Jackiewicz, S. Tracogna: A general class of two-step Runge-Kutta methods for ordinary differential equations.SIAM J. Numer. Anal. 32 (1995), 1390–1427. MR 1352196 |
| Reference:
|
[10] Z. Jackiewicz, S. Tracogna: Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations.Numer. Algorithms 12 (1996), 347–368. MR 1402855, 10.1007/BF02142812 |
| Reference:
|
[11] J. M. Sanz-Serna, M. P. Calvo: Numerical Hamiltonian Problems.Chapman & Hall, London-Glasgow-New York, 1994. MR 1270017 |
| . |
