Approximate Solutions of Functional Equations

Details Approximate Solutions of Functional Equations Approximate Solutions of Functional Equations

2011-05-18

arxiv.org/abs/1105.3664v2

J.Phys.A44:405205,2011

Physics

Mathematical Physics

Approximation for extrema of sine iterates added to revised version

Scientific paper

10.1088/1751-8113/44/40/405205

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 {\lambda}x(1-x). Simple functional conjugation by these functions, and their inverses, substantially improves the numerical accuracy of formal series approximations for their continuous iterates.

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