Exponentially accurate Hamiltonian embeddings of symplectic A-stable Runge--Kutta methods for Hamiltonian semilinear evolution equations

Claudia Wulff, Marcel Oliver

We prove that a class of A-stable symplectic Runge--Kutta time semidiscretizations (including the Gauss--Legendre methods) applied to a class of semilinear Hamiltonian PDEs which a…