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182 results on '"Lotfi, Taher"'

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

Author

Akrami, Mostafa, Lotfi, Taher, and Yaghoobi, Farajollah Mohammadi

Subjects
Mathematics - Classical Analysis and ODEs, Mathematics - Functional Analysis
Abstract

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.

Published
2017

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

Author

Salimi, Mehdi, Lotfi, Taher, Sharifi, Somayeh, and Siegmund, Stefan

Subjects
Mathematics - Numerical Analysis
Abstract

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.

Published
2014

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

Author

Sharifi, Somayeh, Salimi, Mehdi, Siegmund, Stefan, and Lotfi, Taher

Subjects
Mathematics - Numerical Analysis
Abstract

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.

Published
2014

37. Constructing an efficient multi-step iterative scheme for nonlinear system of equations.

Author

Lotfi, Taher and Momenzadeh, Mohammad

Subjects
NONLINEAR systems, ITERATIVE methods (Mathematics), PARTIAL differential equations, DERIVATIVES (Mathematics), QUOTIENT rule
Abstract

The objective of this research is to propose a new multi-step method in tackling a system of nonlinear equations. The constructed iterative scheme achieves a higher rate of convergence whereas only one LU decomposition per cycle is required to proceed. This makes the efficiency index to be high as well in contrast to the existing solvers. The usefulness of the presented approach for tackling differential equations of nonlinear type with partial derivatives is also given. [ABSTRACT FROM AUTHOR]

Published
2021
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38. On the local superconvergence of the fully discretized multiprojection method for weakly singular Volterra integral equations of the second kind

Author

BEYRAMI, Hossein and LOTFI, Taher

Subjects
Fully discretized multiprojection method,collocation method,weakly singular Volterra integral equations,local convergence,error analysis
Abstract

In this paper, we extend the well-known multiprojection method for solving the second kind of weakly singular Volterra integral equations. We apply this method based on the collocation projection and develop a fully discretized version using appropriate quadrature rules. This method has a superconvergence property that the classic collocation method lacks. Although the new approach results in a significant increase in computational cost, when performing the related matrix-matrix products in parallel the computational time can be reduced. We provide a rigorous mathematical discussion about error analysis of this method. Finally, we present some numerical examples to confirm our theoretical results.

Published
2018

40. On the local convergence of Kung-Traub's two-point method and its dynamics.

Author

Delshad, Parandoosh Ataei and Lotfi, Taher

Subjects
*PIPE flow, *CHEMICAL engineering
Abstract

In this paper, the local convergence analysis of the family of Kung-Traub's two-point method and the convergence ball for this family are obtained and the dynamical behavior on quadratic and cubic polynomials of the resulting family is studied. We use complex dynamic tools to analyze their stability and show that the region of stable members of this family is vast. Numerical examples are also presented in this study. This method is compared with several widely used solution methods by solving test problems from different chemical engineering application areas, e.g. Planck's radiation law problem, natch distillation at infinite reflux, van der Waal's equation, air gap between two parallel plates and flow in a smooth pipe, in order to check the applicability and effectiveness of our proposed methods. [ABSTRACT FROM AUTHOR]

Published
2020
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44. Widening basins of attraction of optimal iterative methods

Author

Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Generalitat Valenciana, Ministerio de Economía, Industria y Competitividad, Bakhtiari, Parisa, Cordero Barbero, Alicia, Lotfi, Taher, Mahdiani, Katayoun, Torregrosa Sánchez, Juan Ramón, Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Generalitat Valenciana, Ministerio de Economía, Industria y Competitividad, Bakhtiari, Parisa, Cordero Barbero, Alicia, Lotfi, Taher, Mahdiani, Katayoun, and Torregrosa Sánchez, Juan Ramón

Abstract

[EN] In this work, we analyze the dynamical behavior on quadratic polynomials of a class of derivative-free optimal parametric iterative methods, designed by Khattri and Steihaug. By using their parameter as an accelerator, we develop different methods with memory of orders three, six and twelve, without adding new functional evaluations. Then a dynamical approach is made, comparing each of the proposed methods with the original ones without memory, with the following empiric conclusion: Basins of attraction of iterative schemes with memory are wider and the behavior is more stable. This has been numerically checked by estimating the solution of a practical problem, as the friction factor of a pipe and also of other nonlinear academic problems.

Published
2017

46. Developing two efficient adaptive Newton‐type methods with memory.

Author

Mohamadi Zadeh, Maryam, Lotfi, Taher, and Amirfakhrian, Majid

Subjects
*NUMERICAL analysis, *MEMORY, *NEWTON-Raphson method
Abstract

In this paper, we derive two general adaptive methods with memory in the class of Newton‐type methods by modifying and introducing one and two self accelerators over a variant of Ostrowski's method. The idea of introducing adaptive self‐accelerator (via all the old information for Newton‐type methods) is new and efficient in order to obtain a higher high efficiency index. Finally, we provide convergence analysis and numerical implementations to show the feasibility and applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

Published
2019
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47. New efficient methods for solving nonlinear systems of equations with arbitrary even order

Author

Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Ministerio de Economía y Competitividad, Abbasbandy, Saeid, Bakhtiari, Parisa, Cordero Barbero, Alicia, Torregrosa Sánchez, Juan Ramón, Lotfi, Taher, Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Ministerio de Economía y Competitividad, Abbasbandy, Saeid, Bakhtiari, Parisa, Cordero Barbero, Alicia, Torregrosa Sánchez, Juan Ramón, and Lotfi, Taher

Abstract

In 2011, Khattri and Abbasbandy developed an optimal two-step Jarratt-like method for approximating simple roots of a nonlinear equation. We develop their method for solving nonlinear systems of equations. The main feature of the extended methods is that it uses only one LU factorization which preserves and reduces computational complexities. Following this aim, the suggested method is generalized in such a way that we increase the order of convergence but we do not need new LU factorization. Convergence and complexity analysis are provided rigorously. Using some small and large systems, applicability along with some comparisons are illustrated.

Published
2016

48. Real and complex dynamics of iterative methods

Author

Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Cordero Barbero, Alicia, Torregrosa Sánchez, Juan Ramón, Neta, Beny, Lotfi, Taher, Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Cordero Barbero, Alicia, Torregrosa Sánchez, Juan Ramón, Neta, Beny, and Lotfi, Taher

Published
2016

49. Some new bi-accelerator two-point methods for solving nonlinear equations

Author

Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Islamic Azad University, Hamedan, Cordero Barbero, Alicia, Lotfi, Taher, Torregrosa Sánchez, Juan Ramón, Assari, Paria, Mahdiani, Katayoun, Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Islamic Azad University, Hamedan, Cordero Barbero, Alicia, Lotfi, Taher, Torregrosa Sánchez, Juan Ramón, Assari, Paria, and Mahdiani, Katayoun

Abstract

In this work, we extract some new and efficient two-point methods with memory from their corresponding optimal methods without memory, to estimate simple roots of a given nonlinear equation. Applying two accelerator parameters in each iteration, we try to increase the convergence order from four to seven without any new functional evaluation. To this end, firstly we modify three optimal methods without memory in such a way that we could generate methods with memory as efficient as possible. Then, convergence analysis is put forward. Finally, the applicability of the developed methods on some numerical examples is examined and illustrated by means of dynamical tools, both in smooth and in nonsmooth functions.

Published
2016

50. Real and Complex Dynamics of Iterative Methods

Author

Naval Postgraduate School (U.S.), Applied Mathematics, Neta, Beny, Cordero, Alicia, Torregrosa, Juan R., Lotfi, Taher, Naval Postgraduate School (U.S.), Applied Mathematics, Neta, Beny, Cordero, Alicia, Torregrosa, Juan R., and Lotfi, Taher

Published
2016

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