Iterative methods of order four and five for solving non-linear system : A study on local convergence (original) (raw)

In this paper, we develop the local convergence analysis of Newton-like fourth and fifth order iterative methods for solving a system of non-linear equations. Earlier studies as in Petkovic (Multipoint methods for solving nonlinear equations, Elsevier, Amsterdam,2013), Traub (Iterative methods for the solution of equations, AMS Chelsea Publishing, Providence, 1982) and Kalyanasundaram et al (International Journal of Applied and Computational Mathematics 3 3:2213-2230, 2017) shows that the local convergence was proved using Taylor series expansion which involved the computation of derivatives of order higher than one. For the fourth and fifth order iterative methods under consideration in this paper, it is required that the functions should be at least five and six times differentiable respectively so that the method is applicable to find the solution. This restricts the applicability of the method and also the cost in finding the solution increases as it involves the computation of ...