Abstract:
This thesis concentrates on developing a Modi ed Iterative Method for
computing the approximate solutions of nonlinear equations. We discus the
concept of Error Analysis, Errors in Numerical Methods, Approximation
and Convergence. Newton's method is discussed and proved. This study is
set out to construct or develop a Modi ed Iterative Method for computing
the approximate solutions of nonlinear equations by using Taylor Series
expansion and Adomian Decomposition Method (ADM). The Taylor series
is used in this study due to its higher possibility of convergence since it is
a power series. In the same vain, the Adomian Decomposition method is a
semi analytical method which decomposes the nonlinear equations into a
series of functions thereby making the convergence of these functions much
easier. The convergence of this method is proved to be of order 2. The
Modi eld Iterative Method is a modi cation based on Newton - Raphson's
method. Matlab R2020a is used to compute the solutions of some numerical
examples with the proposed modi ed method. The computation of the
approximated solutions of the method are compared with some existing
iterative methods in literature such as Newton's method, Karthikeyan's
method and External Touch Algorithm method. Then we discussed the
accuracy of the proposed modi ed iterative method when applied to single
variable nonlinear equations. The study pointed out that, the modi ed
method is comparable with the existing methods. Finally we concluded
that the modi ed iterative method is more accurate than the Newton's
method, the External Touch Algorithm method and even to some extent,
the Karthikeyen's method.
