ABSTRACT
The study will investigate development and analysis of new iterative schemes for solving nonlinear equation. The following objectives will guide the study: To review iterative schemes between 1998 and 2012 which have been developed from Adomian decomposition method, Homotopy perturbation method and variants of Newton-Raphson’s method for solving nonlinear equations, to develop new schemes that could compete with previous schemes and probably have further advantages and to compare the new schemes with the existing known iterative schemes.. The study will employ nonlinear polynomials series analysis
INTRODUCTION
Solving nonlinear equations is an important part of numerical analysis. In recent years, interests have grown considerably in developing effective iterative methods (IM) for computing solutions for large systems in science and engineering. The development of faster and more robust IM and preconditions which can be efficiently mapped to a variety of problems is of fundamental importance in that it will be of great assistance to scientists and engineers throughout many disciplines. In numerical analysis this approach is in contrast to direct methods which attempt to solve the problem by a finite sequence of operations. Numerical analysis assumes this task, and with it the limitations of practical calculations. Numerical answers are usually tentative and, at best, known to be accurate only to within certain bounds. IM are often useful even for linear problems involving a large number of variables, where direct methods would be prohibitively expensive. Intuitively iterative methods keep on improving upon subsequent iterations. With iteration methods, the operational cost can often bereduced.
In this thesis, we study iterative methods for solving nonlinear equations, f x 0,
where
f xis any continuously differentiable real valued function. The iterative methods we try to develop for this class of equations will require knowledge of initial guess for desired roots of the equation.
This material content is developed to serve as a GUIDE for students to conduct academic research
A PROPOSAL ON DEVELOPMENT AND ANALYSIS OF NEW ITERATIVE SCHEMES FOR SOLVING NONLINEAR EQUATIONS
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