Higher Order Multipoint Method for Solving Non-Linear Equations

Abstract

The present thesis has been divided into three chapters including the introduction. In chapter one, we include basic results and definitions related to the iterative methods to solve nonlinear equations in the single variable. In chapter two, we reviewed a paper concerning third order iterative methods for multiple roots of nonlinear equations. Several numerical problems arising from real life applications have been included in the chapter to show the efficiency of the proposed scheme. In chapter three, a wide general class of optimal eighth-order methods for multiple zeros with known multiplicity is brought forward, which is based on weight function technique involving function-to-function ratio. An extensive convergence analysis is demonstrated to establish the eighth-order of the developed methods. The numerical experiments considered the superiority of the new methods for solving concrete variety of real life problems coming from different disciplines such as trajectory of an electron in the air gap between two parallel plates, the fractional conversion in a chemical reactor, continuous stirred tank reactor problem, Planck’s radiation law problem, which calculates the energy density within an isothermal blackbody and the problem arising from global carbon dioxide model in ocean chemistry, in comparison with methods of similar characteristics appeared in the literature.