DEVELOPMENT AND ANALYSIS OF NEW ITERATIVE SCHEMES FOR SOLVING NONLINEAR EQUATIONS
DEVELOPMENT AND ANALYSIS OF NEW ITERATIVE SCHEMES FOR SOLVING NONLINEAR EQUATIONS
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Date
2014-08
Authors
MUHAMMAD, SHAKUR NDAYAWO
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Abstract
In this thesis, we have developed two new iterative schemes for solving nonlinear equations.
The two schemes have been constructed from Taylor’s series expansion and Adomian
decomposition method. The two schemes have been compared with other existing iterative
methods using one way analysis of variance (ANOVA). They are found to be efficient and
better than some of the existing schemes. The results show that Newton-Raphson method and
New scheme 1 have more advantage with a maximum of seven iterations each, while new
scheme 2 has nine. Basto et al. and Abbasbany have equal number of thirteen iterations each.
The Adomian has sixteen iterations. Thirty numerical examples are given and solved to justify
the efficiency of the new iterative schemes.
Description
A THESIS SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES,
AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA IN PARTIAL FULFILMENT
OF THE REQUIREMENT FOR THE AWARD OF MASTER OF SCIENCE DEGREE
IN MATHEMATICS.
DEPARTMENT OF MATHEMATICS,
AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA
AUGUST, 2014
Keywords
DEVELOPMENT, ANALYSIS, ITERATIVE, SCHEMES, NONLINEAR EQUATIONS