90 citations · 370 across the 42 of their papers we have counts for
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Hamiltonian interpolation of splitting approximations for nonlinear PDEs
Erwan Faou, Benoit Grebert
We consider a wide class of semi linear Hamiltonian partial differential equa- tions and their approximation by time splitting methods. We assume that the nonlinearity is polynomia…
Quasi invariant modified Sobolev norms for semi linear reversible PDEs
Erwan Faou, Benoit Grebert
We consider a general class of infinite dimensional reversible differential systems. Assuming a non resonance condition on the linear frequencies, we construct for such systems alm…
Resonances in long time integration of semi linear Hamiltonian PDEs
Erwan Faou, Benoit Grebert
We consider a class of Hamiltonian PDEs that can be split into a linear unbounded operator and a regular non linear part, and we analyze their numerical discretizations by symplect…
Modified energy for split-step methods applied to the linear Schrödinger equation
Arnaud Debussche, Erwan Faou
We consider the linear Schrödinger equation and its discretization by split-step methods where the part corresponding to the Laplace operator is approximated by the midpoint rule.…