A variant of newton's metod based on quadrature formula

Abstract

In this dissertation, the two chapters propose an accelerated iteration method for nding the zeroes of a nonlinear function f : R ! R. While accelerated iterative method for nding the zeros of a nonlinear function have been studied already by Weerakoon Fernando and many others, the proposed technique is an e cient alterna- tive for the existing methods. Moreover this thesis provides a semilocal convergence theorem for variation of Newton's method based on various quadrature rules. Chapter 1 provides a short bird view on various iterative methods for nding the zeros of a nonlinear real valued function. Chapter 2 proposes a variant of Newton's method based on Weddle's rule. A local convergence theorem is provided for the proposed iteration. Theoretically a cubic order of convergence is obtained. This section also provides a semilocal convergence theorem for a variant of Newton's method based on various quadrature rules. A comparative numerical study is also provided to support the theory.