In this thesis, two new methods for solution of nonlinear system of equations f(x) = 0 using
two decomposition techniques are established, first is Adomian decomposition technique and
second is Varsha decomposition technique. We expand f(x) to second order then apply both of
these techniques one by one. The convergence order of both these algorithms is three and
efficiency index is p
1/d
=1.442.
The main benefit of this scheme is that we get root of function even after one or two
iterations, obviously has minimum computational complexity as compare to previous systems.
Both methods almost give the same results and convergence orders.
In practice, for large scale problems, many iterative methods can be derived by using two
decomposition techniques with some modifications in Newton Raphson method.
The order of convergence of new iteration formulas can be derived analytically and with the
help of Maple. Some examples are given to illustrate the performance and precision of new
algorithms. These algorithms can be assumed as generalization of old methods for solving
nonlinear equations.