High-order Structure-preserving Methods for Damped Hamiltonian System

We present a novel methodology for constructing arbitrarily high-order structure-preserving methods tailored for damped Hamiltonian systems. This method combines the idea of exponential integrator and energy-preserving collocation methods, effectively preserving the energy dissipation ratio introduced by the damping terms. We demonstrate the conservative properties of these methods and confirm their order of accuracy through numerical experiments involving the damped Burger's equation and Korteweg-de-Vries equation.