In this paper, we present a class of new iterative methods, in which f ′(x) = 0 in some points is permitted. Analysis of convergence shows that the new methods are cubically convergent. Per iteration the new methods require one evaluation of the function and two of its first derivative, but no evaluations of its second derivative. Thus, the new methods have definite practical utility, which is ...

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...

In this paper, we propose a new one-parameter family of Schröder’s method for finding the multiple roots of nonlinear equations numerically. Further, we derive many new cubically convergent families of Schröder-type methods. Proposed families are derived from the modified Newton’s method for multiple roots and one-parameter family of Schröder’s method. Furthermore, we introduce new families of ...

Abstract Direct search methods represent a robust and reliable class of algorithms for solving black-box optimization problems. In this paper, the application those strategies is exported to Riemannian optimization, wherein minimization be performed with respect variables restricted lie on manifold. More specifically, classic linesearch extrapolated variants direct are considered, tailored devi...