New IIR digital differintegrators (differentiator and integrator) with very minor absolute relative errors are presented in this paper. The digital integrator is designed by interpolating some of the existing integrators. The optimum value of the interpolation ratio is obtained through linear programming optimization. Subsequently, by modifying the transfer function of the proposed integrator a...

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...