This thesis consists of three parts. Part I: Theoretical study on conjugate symplecticity of B-series integrators. Algebraic criteria for conjugate symplecticity up to a certain order are presented in terms of the coefficients of the B-series. These criteria are then applied to characterize the conjugate symplecticity of implicit Runge–Kutta methods and of energy-preserving collocation methods. Part II: Partitioned Runge-Kutta-Chebyshev methods for diffusion-advection-reaction problems. We discuss an integration method based on Runge–Kutta–Chebyshev methods that is designed to treat moderately stiff and non-stiff terms separately. The method, called PRKC, is a one-step, explicit partitioned Runge–Kutta method of second-order with extended real stability interval. Part III: Characterization of Poisson integrators. Series expansions like B-series play a central role in the numerical analysis of ODEs. Part III introduces a new extension of B-series, called P-series, dedicated to integrators for a generalization of Hamiltonian systems, called Poisson systems.