Order conditions for G-symplectic methods
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| 024 | 7 | 0 | |a 10.1007/s10543-014-0541-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10543-014-0541-x | ||
| 245 | 0 | 0 | |a Order conditions for G-symplectic methods |h [Elektronische Daten] |c [John Butcher, Gulshad Imran] |
| 520 | 3 | |a General linear methods for the solution of ordinary differential equations are both multivalue and multistage. The order conditions will be stated and analyzed using a B-series approach. However, imposing the G-symplectic structure modifies the nature of the order conditions considerably. For Runge-Kutta methods, rooted trees belonging to the same tree have equivalent order conditions; if the trees are superfluous, they are automatically satisfied and can be ignored. For G-symplectic methods, similar results apply but with a more general interpretation. In the multivalue case, starting conditions are a natural aspect of the meaning of order; unlike the Runge-Kutta case for which "effective order” or "processing” or "conjugacy” has to be seen as having an artificial meaning. It is shown that G-symplectic methods with order 4 can be constructed with relatively few stages, $$s=3$$ s = 3 , and with only $$r=2$$ r = 2 inputs to a step. | |
| 540 | |a Springer Science+Business Media Dordrecht, 2015 | ||
| 690 | 7 | |a G-symplectic methods |2 nationallicence | |
| 690 | 7 | |a Order conditions |2 nationallicence | |
| 690 | 7 | |a Conformability |2 nationallicence | |
| 690 | 7 | |a Trees |2 nationallicence | |
| 690 | 7 | |a Rooted trees |2 nationallicence | |
| 700 | 1 | |a Butcher |D John |u Department of Mathematics, University of Auckland, Auckland, New Zealand |4 aut | |
| 700 | 1 | |a Imran |D Gulshad |u Department of Mathematics, University of Auckland, Auckland, New Zealand |4 aut | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/4(2015-12-01), 927-948 |x 0006-3835 |q 55:4<927 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0541-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0541-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Butcher |D John |u Department of Mathematics, University of Auckland, Auckland, New Zealand |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Imran |D Gulshad |u Department of Mathematics, University of Auckland, Auckland, New Zealand |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/4(2015-12-01), 927-948 |x 0006-3835 |q 55:4<927 |1 2015 |2 55 |o 10543 | ||