ABSTRACT
A plethora of problems from diverse disciplines such as Applied Mathematics, Mathematical Biology, Chemistry, Economics, Physics and also Engineering reduce to solving equations using numerical methods, since closed form solutions are rarely attainable. Recently there has been a surge in the study of high convergence order methods. Looking at this direction, we develop a sixth convergence order method with parameters. The convergence was first shown before using hypotheses up to the seventh derivative not appearing in these methods. But this way the applicability of these methods is limited. That is why we present a local convergence analysis based only on the first derivative, which actually appears in these methods. That is how we extend their applicability.
Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study. This fact allows us to enlarge the number and type of problems that can be solved by means of using these methods, including differential equations which are one of the most challenging problems in optimization and modelling areas. Concrete examples of the theoretical results are also presented in this chapter.
