SOLUTION OF NON-LINEAR EQUATION USING AN ITERATIVE METHOD BASED ON MIXED QUADRATURE

摘要

In this article , we advocate an excellent refinement to the Newton's iteration scheme for the solution of non-linear equations. This refinement necessitates a quadrature of relatively higher precision for handling the integral occurring in course of derivation of new iterative scheme. A very convenient way to achieve the enhanced precision is that of mixed quadrature. Through convergence analysis, we have shown theoretically that the new scheme is more powerful than the old one. Also the comparative study of numerical results in respect of some test equations agrees with the theoretical predictions of the new scheme.