Interpolation predictors over implicitly defined curves

The aim of this paper is to present some higher-order predictors methods for the numerical tracing of implicitly defined curves. Two higher-order predictors are described based upon the Newton and Hermite interpolation polynomials using previously computed points on the curve to compute the coefficients via divided differences. Some applications are made to the numerical integration of closed implicitly defined curves. The line integral is approximated via a Gauss-Legendre quadrature of the interpolating polynomial.