s method when the majorant principle of Kantorovich is applied to operators with high order derivatives satisfying a center Lipschitz type condition, so that we extend the classical conditions of these type, that are centered at the starting point of Newton’s method, to other points belonging ...
Inserting the derived interpolation formulas into the triple Newton method, the eighth-order optimal iterative schemes are constructed, of which four evaluations of functions per iteration are required. Keywords: nonlinear equation; two-dimensional approach; fractional iterative scheme; modified derivative-...
Newton’s method; local convergence; convergence order; fractal; basins of attraction 1. Introduction Let F be the differentiable mapping of a convex subset D of a Banach space X to itself. We deal with the convergence of the sixth-order Contraharmonic-mean method (CHN) [1] ⎧⎩⎨ ...
In the presented article a generalization of Newton’s formula for the shear stress in a fluid is carried out by giving it a power-law form. After the introduction of the corresponding strain rate tensor, a generalization is made to the spatial case of flow and the rheological relation is ...