Runge-Kutta methods and renormalization

Abstract

A connection between the algebra of rooted trees used in renormalization theory and Runge-Kutta methods is pointed out. Butcher's group and B-series are shown to provide a suitable framework for renormalizing a toy model of field the ory, following Kreimer's approach. Finally B-series are used to solve a class of non-linear partial differential equations.

LaTeX file with FeynMF package. 21 pages, no figure

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