2007/06/30 by C. Bervillier, B. Boisseau, Héctor Giacomini +1
Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Boundary value problem #Differential equation #Electromagnetic Simulation and Numerical Methods #Field (mathematics) #Hypergeometric distribution #Hypergeometric function #Mathematical analysis #Mathematical physics #Mathematics #Numerical methods for differential equations #Ordinary differential equation #Pure mathematics #Renormalization group #Theoretical and Computational Physics #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2007.07.005
published as Nucl.Phys.B789:525-551,2008 · Final version to appear in Nucl. Phys. B. Some references added correctly
openalex publication_date 2007/07/20 · arxiv created 2007/10/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).