caa a22 4500 605497036 CHVBK 20210128100539.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10543-014-0541-x doi (NATIONALLICENCE)springer-10.1007/s10543-014-0541-x Order conditions for G-symplectic methods [Elektronische Daten] [John Butcher, Gulshad Imran] 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. Springer Science+Business Media Dordrecht, 2015 G-symplectic methods nationallicence Order conditions nationallicence Conformability nationallicence Trees nationallicence Rooted trees nationallicence Butcher John Department of Mathematics, University of Auckland, Auckland, New Zealand aut Imran Gulshad Department of Mathematics, University of Auckland, Auckland, New Zealand aut BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 927-948 0006-3835 55:4<927 2015 55 10543 https://doi.org/10.1007/s10543-014-0541-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0541-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Butcher John Department of Mathematics, University of Auckland, Auckland, New Zealand aut NATIONALLICENCE 700 1- Imran Gulshad Department of Mathematics, University of Auckland, Auckland, New Zealand aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 927-948 0006-3835 55:4<927 2015 55 10543