Abstract We rewrite abstract delay equations as nonautonomous Cauchy problems allowing us to introduce a Magnus-type integrator for the former. prove second-order convergence of obtained integrator. also show that if differential operators involved admit common invariant set their generated semigroups, then will respect this well, much weaker assumptions obtain desired convergence. As an illust...

We examine a new second-order integrator recently found by Omelyan et al. The integration error of the new integrator measured in the root mean square of the energy difference, 1/2, is about 10 times smaller than that of the standard second-order leapfrog (2LF) integrator. As a result, the step size of the new integrator can be made about three times larger. Taking into account a facto...

A Hermite fitted block integrator (HFBI) for numerically solving second-order anisotropic elliptic partial differential equations (PDEs) was developed, analyzed, and implemented in this study. The method derived through collocation interpolation techniques using the polynomial as basis function. interpolated at first two successive points, while occurred all suitably chosen points. major scheme...

The paper presents a summary of different double second-order generalized integrator (DSOGI)-based phase-locked loop (PLL) algorithms for synchronization with three-phase weak grids. methods are compared through simulation under variety grid conditions, such as unbalanced phase voltages, high low-order harmonics distortion, frequency steps, jumps, and voltage sags. Following the results, three ...