Considered are numerical integration schemes for nondissipative dynamical systems in which multiple time scales are present. It is assumed that one can do an explicit separation of the RHS “forces”… (More)

Many existing numerical schemes for evolutionary problems in partial differential equations (PDEs) can be viewed as method of lines (MOL) schemes. This paper treats the convergence of one-step MOL… (More)

We show how B-series may be used to derive in a systematic way the analytical expressions of the high-order stroboscopic averaged equations that approximate the slow dynamics of highly oscillatory… (More)

In an effort to avoid random-walk behaviour, many Markov Chain Monte Carlo methods use proposals based on dynamics related to the target distribution. The Hybrid Monte Carlo (HMC) is based on… (More)

By means of a two-frequency test problem, we analyze the instabilities and inaccuracies that may impair the performance of multiple time steps/split operator integrators in highly oscillatory… (More)

In 1991 Rowlands proposed an effectively fourth-order, effectively two-stage, explicit symplectic integrator based on using a Hessian–vector product to modify the force evaluation in the leapfrog… (More)