Polynomial Maps

The step-size-controlled polynomial model is presented as a promising strictly polynomial framework where numerical resolution is explicit. Fixed discrete polynomial maps cannot uniformly provide the autonomous continuous mechanisms available to polynomial ODEs. The Euler discretization turns a polynomial ODE into a polynomial map by storing the step size as a coordinate. A primitive recursive threshold on step size is chosen so that Euler simulation stays within the robust output margin. Step-size-controlled polynomial maps use a fixed rational polynomial map with an externally supplied dyadic step size and primitive recursive thresholds.