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

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

We prove that a class of A-stable symplectic Runge–Kutta time semi-discretizations (including the Gauss–Legendre methods) applied to a class of semilinear Hamiltonian partial differential equations (PDEs) that are well posed on spaces of analytic functions with analytic initial data can be embedded into a modified Hamiltonian flow up to an …