Abstract:
Various problems of pure and applied sciences such as physics, chemistry, biology,
engineering, economics, management sciences, industrial research and optimization can
be studied in the unified frame work of the system of nonlinear equations. In this thesis,
we develop several new iterative methods for solving a system of nonlinear equations by
using different techniques, including quadrature technique, new decomposition method
and variational iteration technique. We prove the convergence of the new methods. We
obtain the upper bounds of the error of new methods. We also discuss the efficiency
index of the proposed methods and compare it with some other well-known methods. We
provide several examples for the implementation and performance of the new methods.
Comparison with some other existing methods is also given. We also discuss some open
research problems.
