  Extreme benchmarks of ten or more places for the point kinetics equations for
time dependent nuclear reactor power transients are rare. Therefore, to
establish an extreme benchmark, we will employ a Taylor series with continuous
analytical continuation (CAC) to solve the ordinary differential equations of
point kinetics including feedback. Non-linear Wynn-epsilon convergence
acceleration confirms the highly precise solutions for neutron and precursor
densities. Through adaptive partitioning of time intervals, the proposed
Converged Accelerated Taylor Series, or CATS algorithm [1] in double precision,
automatically performs successive mesh refinement to obtain high precision
initial conditions for each sub-interval, with the intent to reduce propagation
error. Confirmation of ten to twelve places comes from comparison to the BEFD
(Backward Euler Finite Difference) algorithm [2] in quadruple precision also
developed by the author. We report benchmark results for common cases found in
the literature including step, ramp, zigzag and sinusoidal prescribed
reactivity insertions and insertions with non-linear adiabatic Doppler
feedback. We also establish a suite of new prescribed reactivity insertions and
insertions with feedback, based on reactivities with Taylor series as suggested
by the CATS algorithm.
