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Study of local convergence and dynamics of a king-like two-step method with applications
(Mathematics, 2020-07-01)
In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because ...
Weaker conditions for inexact mutitpoint Newton-like methods
(Journal of Mathematical Chemistry, 2020-01)
In this paper we study the problem of analyzing the convergence both local and semilocal of inexact Newton-like methods for approximating the solution of an equation in which there exists nondifferentiability. We will ...
Extending the Applicability of Stirling's Method
(Mathematics, 2020-01)
Stirling's method is considered as an alternative to Newton's method when the latter fails to converge to a solution of a nonlinear equation. Both methods converge quadratically under similar convergence criteria and require ...
A new technique for studying the convergence of Newton’s solver with real life applications
(Journal of Mathematical Chemistry, 2020-04)
The convergence domain for both the local and semilocal case of Newton’s method for Banach space valued operators is small in general. There is a plethora of articles that have extended the convergence criterion due to ...
Convergence and Dynamics of a Higher-Order Method
(Symmetry, 2020-03)
Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves ...