Abstract
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.
Original language | English |
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Pages (from-to) | 1067-1076 |
Number of pages | 10 |
Journal | Computers and Mathematics with Applications |
Volume | 44 |
Issue number | 8-9 |
DOIs | |
Publication status | Published - Oct 2002 |
Keywords
- Gaussian quadrature
- Higher-order predictor
- Implicitly defined curve
- Interpolating polynomial
- Line integral
ASJC Scopus subject areas
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics