A NEW NEWTON-TYPE METHOD FOR SOLVING BOTH NON-LINEAR EQUATIONS AND SYSTEMS
GREGORY ANTONI *
Aix-Marseille Universite, IFSTTAR, LBA UMR T24, F-13016 Marseille, France
*Author to whom correspondence should be addressed.
This study concerns the development of a new Newton-type method in order to solve both with non-linear equations and systems. The main idea for this method is that it takes into account an approximation of terms of order higher than one in Taylor's series associated with non-linear equations. In the case of systems of non-linear equations, this new modied Newton's method is coupled with a Gauss-Seidel's method for reducing the non-linear system under consideration to solve non-linear equations independently with only one variable. The presented method is tested and discussed on some examples.
Keywords: Newton's method, non-linear equations and systems, taylor series, Gauss-Seidel's method