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The relation between the Wilson-Polchinski and the Litim optimized ERGEs inthe local potential approximation is studied with high accuracy using twodifferent analytical approaches based on a field expansion: a recently proposedgenuine analytical approximation scheme to two-point boundary value problems ofordinary differential equations, and a new one based on approximating thesolution by generalized hypergeometric functions. A comparison with thenumerical results obtained with the shooting method is made. A similar accuracyis reached in each case. Both two methods appear to be more efficient than theusual field expansions frequently used in the current studies of ERGEs (inparticular for the Wilson-Polchinski case in the study of which they fail).

Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation