caa a22 4500 445331623 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s10208-011-9094-4 doi (NATIONALLICENCE)springer-10.1007/s10208-011-9094-4 Hamiltonian Interpolation of Splitting Approximations for Nonlinear PDEs [Elektronische Daten] [Erwan Faou, Benoît Grébert] We consider a wide class of semilinear Hamiltonian partial differential equations and their approximation by time splitting methods. We assume that the nonlinearity is polynomial, and that the numerical trajectory remains at least uniformly integrable with respect to an eigenbasis of the linear operator (typically the Fourier basis). We show the existence of a modified interpolated Hamiltonian equation whose exact solution coincides with the discrete flow at each time step over a long time. While for standard splitting or implicit-explicit schemes, this long time depends on a cut-off condition in the high frequencies (CFL condition), we show that it can be made exponentially large with respect to the step size for a class of modified splitting schemes. SFoCM, 2011 Hamiltonian interpolation nationallicence Backward error analysis nationallicence Splitting integrators nationallicence Nonlinear Schrödinger equation nationallicence Nonlinear wave equation nationallicence Long-time behavior nationallicence Faou Erwan INRIA & ENS Cachan Bretagne, Avenue Robert Schumann, 35170, Bruz, France aut Grébert Benoît Laboratoire de Mathématiques Jean Leray, Université de Nantes, 2, rue de la Houssinière, 44322, Nantes cedex 3, France aut Foundations of Computational Mathematics Springer-Verlag 11/4(2011-08-01), 381-415 1615-3375 11:4<381 2011 11 10208 https://doi.org/10.1007/s10208-011-9094-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-011-9094-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Faou Erwan INRIA & ENS Cachan Bretagne, Avenue Robert Schumann, 35170, Bruz, France aut NATIONALLICENCE 700 1- Grébert Benoît Laboratoire de Mathématiques Jean Leray, Université de Nantes, 2, rue de la Houssinière, 44322, Nantes cedex 3, France aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/4(2011-08-01), 381-415 1615-3375 11:4<381 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer