Effective Liouville operators of the firstand the second-order symplectic integrators are obtained for the one-dimensional harmonic-oscillator system. The operators are defined only when the time step is less than two. Absolute values of the coordinate and the momentum monotonically increase for large time steps. PACS numbers: 05.10.-a, 02.10.Hh

This paper presents a Lie-Trotter splitting for inertial Langevin equations (Geometric Langevin Algorithm) and analyzes its long-time statistical properties.The splitting is defined as a composition of a variational integrator with an Ornstein-Uhlenbeck flow. Assuming the exact solution and the splitting are geometrically ergodic, the paper proves the discrete invariant measure of the splitting...

This paper presents the modified integrator which we can use in the controlling scheme of an induction motor (IM). The modification tends to some advancement in direct torque control of induction motor. The undesirable variations which occur in the form of offset, gain error, etc can be eliminate by means of the involvement of the new integrator in the direct torque and flux control (DTFC) meth...

In this paper, we derive the impulse response of the distributed order integrator/ differentiator and its asymptotic property by using the complex path integral. Based on the derived analytical impulse response, we present a technique to perform the discretization of the above distributed order integrator/differentiator. The derived asymptotic property can be applied to verify the feasibility o...

A new explicit time-reversible orbit integrator for the equations of motion in a static homogeneous magnetic field —called Cyclotronic integrator— is presented. Like Spreiter and Walter’s Taylor expansion algorithm, for sufficiently weak electric field gradients this second order method does not require a fine resolution of the Larmor motion; it has however the essential advantage of being symp...

A variable-step double-integration multi-step integrator is derived using divided differences. The derivation is based upon the derivation of Shampine-Gordon, a single-integration method. Variable-step integrators are useful for propagating elliptical orbits, because larger steps can be taken near apogee. As a double-integration method, the integrator performs only one function evaluation per s...