Improved hybrid methods in solving single variable nonlinear algebraic equations / Nor Hanim Abd Rahman

Nonlinear problem is one of the most frequently occurring problems
in scientific works especially in science and engineering applications.
Amongst the most popular schemes are the Newton’s method and
homotopy perturbation method. However, the duration to converge are
heavily depends on how close the guess value is to the real root/s and the
rate of convergence for Newton’s method is only order-2 and its efficiency
index is only ≈ 1.41421. Secondly, some of the methods utilized
successive approximation procedure to ensure every step of computing
will converge to the desired root and one of the most common problems is
the improper initial values for the iterative methods. Thus, this particular
research aims to develop an improved numerical solution for solving
nonlinear equations by using hybrid concept and higher order correctional
terms. Higher order successive approximations are applied and evaluated
to ensure it converges to the desired root/s more effectively..