A family of iterative methods that uses divided differences of first and second orders
This paper extends a biparametric family of fourth-order Steffensen-type derviative-free iterative methods that uses multidimensional divided differences of first and second orders for solving systems of nonlinear equations. In considering the computational efficiency, two optimal methods are identified. The semilocal convergence of one of these optimal methods is studied by using a technique based on recurrence relations. A numerical example of a system of nonlinear equations that arises from a process of discretization of a nonlinear integral equation of mixed Hammerstein type is used to demonstrate the theoretical results.
fourth-order Steffensen-type derviative-free iterative methods
nonlinear integral equation of mixed Hammerstein type
scientific article; zbMATH DE number 6510061
scientific article