arXiv subjects

Taher Lotfi

Publications and source records attributed to Taher Lotfi.

3 recordsLinked to original sources

arXiv2017

A new effective weighted modified perturbation technique for solving a class of hypersingular integral equations

This paper is an attempt to solve an important class of hypersingular integral equations of the second kind. To this end, we apply a new weighted and modified perturbation method which includes some special cases of the Adomian decomposition method. To justify the efficiency and applicability of the proposed method, we examine some examples. The principal aspects of this method are its simplicity along with fast computations.

math.CA↗

arXiv2014

Optimal Newton-Secant like methods without memory for solving nonlinear equations with its dynamics

We construct two optimal Newton-Secant like iterative methods for solving non-linear equations. The proposed classes have convergence order four and eight and cost only three and four function evaluations per iteration, respectively. These methods support the Kung and Traub conjecture and possess a high computational efficiency. The new methods are illustrated by numerical experiments and a comparison with some existing optimal methods. We conclude with an investigation of the basins of attraction of the solutions in the complex plane.

math.NA↗

arXiv2014

A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations

We introduce a new class of optimal iterative methods without memory for approximating a simple root of a given nonlinear equation. The proposed class uses four function evaluations and one first derivative evaluation per iteration and it is therefore optimal in the sense of Kung and Traub's conjecture. We present the construction, convergence analysis and numerical implementations, as well as comparisons of accuracy and basins of attraction between our method and existing optimal methods for several test problems.

math.NA↗