Papers by Somayeh Sharifi
SeMA journal, Oct 27, 2016
In this paper, we construct an iterative method with memory based on the Newton-Secants method to... more In this paper, we construct an iterative method with memory based on the Newton-Secants method to solve nonlinear equations. This proposed method has fourth order convergence and costs only three functions evaluation per iteration and without any evaluation of the derivative function. Acceleration of the convergence speed is achieved by an appropriate variation of a free parameter in each step. This self-accelerator parameter is estimated using Newtons interpolation polynomial of third degree. The order of convergence is increased from 4 to 5.23 without any extra function evaluation. This method has the efficiency index equal to 5.2313≈1.7358. We describe the analysis of the proposed method along with numerical experiments including comparison with the existing methods. Finally, the attraction basins of the proposed method are shown and compared with other existing methods.
Japan Journal of Industrial and Applied Mathematics, Jan 6, 2018
In this study, a three-point iterative method for solving nonlinear equations is presented. The p... more In this study, a three-point iterative method for solving nonlinear equations is presented. The purpose is to upgrade a fourth order iterative method by adding one Newton step and using a proportional approximation for last derivative. Per iteration this method needs three evaluations of the function and one evaluation of its first derivatives. In addition, the efficiency index of the developed method is √4 8 ≈ 1.682 which supports the Kung-Traub conjecture on the optimal order of convergence. Moreover, numerical and graphical comparison of the proposed method with other existing methods with the same order of convergence are given.
arXiv (Cornell University), Oct 9, 2014
We introduce a new class of optimal iterative methods without memory for approximating a simple r... more 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.
Dynamic Games and Applications, Jun 5, 2015
In this paper we investigate a differential game in which countably many dynamical objects pursue... more In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to integral constraints, and the controls of the other pursuers and the evader are subject to geometric constraints. The payoff of the game is the distance between the evader and the closest pursuer when the game is terminated. We construct optimal strategies for players and find the value of the game.
Calcolo, May 9, 2015
In this paper, we present an iterative three-point method with memory based on the family of King... more In this paper, we present an iterative three-point method with memory based on the family of King's methods to solve nonlinear equations. This proposed method has eighth order convergence and costs only four function evaluations per iteration which supports the Kung-Traub conjecture on the optimal order of convergence. An acceleration of the convergence speed is achieved by an appropriate variation of a free parameter in each step. This self accelerator parameter is estimated using Newton's interpolation polynomial of fourth degree. The order of convergence is increased from 8 to 12 without any extra function evaluation. Consequently, this method, possesses a high computational efficiency. Finally, a numerical comparison of the proposed method with related methods shows its effectiveness and performance in high precision computations.
arXiv (Cornell University), Nov 12, 2014
In this paper, we present a family of three-point with eight-order convergence methods for findin... more In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. This class of methods has the efficiency index equal to 8 1 4 ≈ 1.682. We describe the analysis of the proposed methods along with numerical experiments including comparison with existing methods.
arXiv (Cornell University), Jul 13, 2015
In this paper, we modify the Newton-Secant method with third order of convergence for finding mul... more In this paper, we modify the Newton-Secant method with third order of convergence for finding multiple roots of nonlinear equations. Per iteration this method requires two evaluations of the function and one evaluation of its first derivative. This method has the efficiency index equal to 3 1 3 ≈ 1.44225. We describe the analysis of the proposed method along with numerical experiments including comparison with existing methods. Moreover, the dynamics of the proposed method are shown with some comparisons to the other existing methods. Keywords Multi-point iterative methods • Newton-Secant method • multiple roots • Basin of attraction.
arXiv (Cornell University), Aug 7, 2015
In this paper, we present a three-point without memory iterative method based on Kung and Traub's... more In this paper, we present a three-point without memory iterative method based on Kung and Traub's method for solving non-linear equations in one variable. The proposed method has eighthorder convergence and costs only four function evaluations each iteration which supports the Kung-Traub conjecture on the optimal order of convergence. Consequently, this method possesses very high computational efficiency. We present the construction, the convergence analysis, and the numerical implementation of the method. Furthermore, comparisons with some other existing optimal eighthorder methods concerning accuracy and basins of attraction for several test problems will be given.
Japan Journal of Industrial and Applied Mathematics, Nov 9, 2016
We present a three-point iterative method without memory for solving nonlinear equations in one v... more We present a three-point iterative method without memory for solving nonlinear equations in one variable. The proposed method provides convergence order eight with four function evaluations per iteration. Hence, it possesses a very high computational efficiency and supports Kung and Traub's conjecture. The construction, the convergence analysis, and the numerical implementation of the method will be presented. Using several test problems, the proposed method will be compared with existing methods of convergence order eight concerning accuracy and basin of attraction. Furthermore, some measures are used to judge methods with respect to their performance in finding the basin of attraction.
A new class of three-point methods with optimal convergence order eight and its dynamics
Numerical Algorithms, May 3, 2014
ABSTRACT We establish a new class of three-point methods for the computation of simple zeros of a... more ABSTRACT We establish a new class of three-point methods for the computation of simple zeros of a scalar function. Based on the two-point optimal method by Ostrowski (1966), we construct a family of order eight methods which use three evaluations of f and one of f' and therefore have an efficiency index equal to and are optimal in the sense of the Kung and Traub conjecture (Kung and Traub J. Assoc. Comput. Math. 21, 634-651, 1974). Moreover, the dynamics of the proposed methods are shown with some comparisons to other existing methods. Numerical comparison with existing optimal schemes suggests that the new class provides a valuable alternative for solving nonlinear equations.
arXiv (Cornell University), Oct 19, 2014
We construct two optimal Newton-Secant like iterative methods for solving non-linear equations. T... more 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.
Afrika Matematika, Feb 14, 2019
In this paper, some iterative methods with third order convergence for solving the nonlinear equa... more In this paper, some iterative methods with third order convergence for solving the nonlinear equation were reviewed and analyzed. The purpose is to find the best iteration schemes that have been formulated thus far. Hence, some numerical experiments and basin of attractions were performed and presented graphically. Based on the five test functions it was found that the best method is D87a due Dong's Family method (
Open Mathematics, 2016
In this paper, we present a family of three-point with eight-order convergence methods for findin... more In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari's method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to 8 1 4 1:682. We describe the analysis of the proposed methods along with numerical experiments including comparison with the existing methods. Moreover, the attraction basins of the proposed methods are shown with some comparisons to the other existing methods.
Nanomaterials, 2022
In this article, we explore how activation energy and varied transit parameters influence the two... more In this article, we explore how activation energy and varied transit parameters influence the two-dimensional stagnation point motion of nano-biofilm of Sutterby fluids incorporating gyrotactic microbes across a porous straining/shrinking sheet. Prior investigations implied that fluid viscosity as well as thermal conductance are temperature based. This research proposes that fluid viscosity, heat capacity and nanofluid attributes are all modified by solute concentration. According to some empirical research, the viscosity as well as heat conductivity of nanoparticles are highly based on the concentration of nanoparticles instead of only the temperature. The shooting approach with the RK-4 technique is applied to acquire analytical results. We contrast our outcomes with those in the existing research and examine their consistency and reliability. The graphic performance of relevant factors on heat, velocity, density and motile concentration domains are depicted and discussed. The ski...
On game value for a pursuit-evasion differential game with state and integral constraints
Japan Journal of Industrial and Applied Mathematics, 2022
Symmetry, 2019
In this study, we present a new higher-order scheme without memory for simple zeros which has two... more In this study, we present a new higher-order scheme without memory for simple zeros which has two major advantages. The first one is that each member of our scheme is derivative free and the second one is that the present scheme is capable of producing many new optimal family of eighth-order methods from every 4-order optimal derivative free scheme (available in the literature) whose first substep employs a Steffensen or a Steffensen-like method. In addition, the theoretical and computational properties of the present scheme are fully investigated along with the main theorem, which demonstrates the convergence order and asymptotic error constant. Moreover, the effectiveness of our scheme is tested on several real-life problems like Van der Waal’s, fractional transformation in a chemical reactor, chemical engineering, adiabatic flame temperature, etc. In comparison with the existing robust techniques, the iterative methods in the new family perform better in the considered test examp...
Dynamic Games and Applications, 2015
In this paper we investigate a differential game in which countably many dynamical objects pursue... more In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to geometric constraints and the controls of the other pursuers and the evader are subject to integral constraints. The payoff of the game is the distance between the evader and the closest pursuer when the game is terminated. We construct optimal strategies for players and find the value of the game. 2010 Mathematics Subject Classification. 91A23.
We introduce a new class of optimal iterative methods without memory for approximating a simple r... more 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.
In this paper, we present a third-order iterative method based on Potra-Pták method to compute th... more In this paper, we present a third-order iterative method based on Potra-Pták method to compute the approximate multiple roots of nonlinear equations. The method requires two evaluations of the function and one evaluation of its first derivative per iteration and it has the efficiency index equal to 3 1 3 ≈ 1.44225. We describe the analysis of the proposed methods along with numerical experiments including comparison with existing methods. Moreover, the attraction basins are shown and compared with other existing methods.
Review of some iterative methods for solving nonlinear equations with multiple zeros
Afrika Matematika
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Papers by Somayeh Sharifi