Solving functional flow equations with pseudospectral methods

We apply pseudospectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations [J. Borchardt and B. Knorr, Phys. Rev. D 91, 105011 (2015)]. The advantages of our method are illustrated with the help of two classes of models: first, to make contact with literature, we investigate flows of the O(N) model in three dimensions, for $N=1$, 4 and in the large N limit. For the case of a fractal dimension, $d=2.4$, and $N=1$, we follow the flow along a separatrix from a multicritical fixed point to the Wilson-Fisher fixed point over almost 13 orders of magnitude. As a second example, we consider flows of bounded quantum-mechanical potentials, which can be considered as a toy model for Higgs inflation. Such flows pose substantial numerical difficulties, and represent a perfect test bed to exemplify the power of pseudospectral methods.