Approximate solutions of functional equations

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 \frac{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.