Approximate Solutions of Functional Equations

Abstract

Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by construction of approximate continuous functional iterates for x/(1-x), sin x, and λx(1-x). Simple functional conjugation by these functions, and their inverses, substantially improves the numerical accuracy of formal series approximations for their continuous iterates.

Approximation for extrema of sine iterates added to revised version