Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
partitioned Runge-Kutta method; ordinary differential equation; order conditions
partitioned Runge-Kutta method; ordinary differential equation; order conditions
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.
References:
[1] M. Abramowitz, I. S. Stegun (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards, Applied Mathematics Series 55, Washington, D.C., 1972. MR 0757537
[2] P. Albrecht: A new theoretical approach to Runge-Kutta methods. SIAM J. Numer. Anal. 24 (1987), 391–406. DOI 10.1137/0724030 | MR 0881373 | Zbl 0617.65067
[3] P. Albrecht: The Runge-Kutta theory in a nutshell. SIAM J. Numer. Anal. 33 (1996), 1712–1735. DOI 10.1137/S0036142994260872 | MR 1411846 | Zbl 0858.65074
[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. DOI 10.1090/S0025-5718-1982-0658219-8 | MR 0658219
[5] E. Griepentrog: Gemischte Runge-Kutta-Verfahren für steife Systeme. In: Seminarbericht Nr. 11, Sekt, Math., Humboldt Univ. Berlin, 1978, pp. 19–29. MR 0540731 | Zbl 0434.65044
[6] E. Hairer: Order conditions for numerical methods for partitioned ordinary differential equations. Numer. Math. 36 (1981), 431–445. DOI 10.1007/BF01395956 | MR 0614858 | Zbl 0462.65049
[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
[8] Z. Jackiewicz, R. Vermiglio: General linear methods with external stages of different orders. BIT 36 (1996), 688–712. DOI 10.1007/BF01733788 | MR 1420272
[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
[10] Z. Jackiewicz, S. Tracogna: Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations. Numer. Algorithms 12 (1996), 347–368. DOI 10.1007/BF02142812 | MR 1402855
[11] J. M. Sanz-Serna, M. P. Calvo: Numerical Hamiltonian Problems. Chapman & Hall, London-Glasgow-New York, 1994. MR 1270017
Search
Partner of
