Anuradha Singh
@iiitn.ac.in
Assistant Professor.
Indian Institute of Information Technology Nagpur
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Anuradha Singh, Ayushi Tandon, and Laasya Cherukuri
Chapman and Hall/CRC
Anuradha Singh
Springer Science and Business Media LLC
In this paper, a new fourth-order iterative scheme for finding the zeros of systems of nonlinear equations has been built and analyzed. Theoretical proof has been given to confirm the convergence order of the new method. The effectiveness of the proposed method is shown by the comparison of traditional as well as flops-like efficiency index with recent existing same order schemes. Numerical examples confirm that the new iterative method is efficient and gives tough competition to some existing fourth-order methods. We have also discussed the application of our proposed method for finding numerical solution of nonlinear ODE and PDE.
Anuradha Singh
Inderscience Publishers
Anuradha Singh
IEEE
One of the most challenging tasks in real life is to find the multiple zeros of nonlinear equations. It is also known that the iterative methods are highly sensitive towards initial guesses. So, the choice of initial guess is also a difficult task with iterative methods. Various researchers have established the generalized form of iterative methods for finding the multiple roots. The prime focus of this study is to extend existing fourth order method from simple roots to multiple roots because some of the available methods for findings multiple root are fails or do not perform well for some nonlinear functions.
Ajaz Ahmad Dar and K. Elangovan
Inderscience Publishers
Anuradha Singh and J. P. Jaiswal
Natural Sciences Publishing
This article concerned with the issue of solving a nonlinear equation with the help of iterative method where no any derivative evaluation is required per iteration. Therefore, this work contributes to a new class of optimal eighth-order Steffensen-type methods. Theoretical proof has been given to reveal the eighth-order convergence. Numerical comparisons have been carried out to show the effectiveness of contributed scheme.
Anuradha Singh and J. P. Jaiswal
Springer Science and Business Media LLC
In the present paper, we propose a new family of the fourth-order iterative methods for finding multiple root of nonlinear equations with known multiplicity. This family is the multiple extension of the existing family for simple root. Some particular cases of proposed method have been also discussed. The presented iterative family requires one function and two derivative evaluations and thus agree with the conjecture of Kung-Traub for the case $$n = 3$$n=3 (i.e. optimal). Numerical comparisons have been carried out to show the performance of the proposed method. Finally, we compare our method with some existing methods by basin of attractions and observe that the proposed scheme is competitive to other existing methods for obtaining multiple root of nonlinear equations.
Anuradha Singh and J. P. Jaiswal
Springer India
The object of the present paper is to improve the R-order convergence of with memory method proposed by Eftekhari (Int J Differ Eqn 2014:6, 2014) [1]. To achieve this goal, one more iterative parameter is introduced, which is calculated with the help of Newton’s interpolatory polynomial of degree five. It is shown that the R-order convergence of the proposed method is increased from 11.2915 to 13.4031 without any extra evaluation. Smooth as well as nonsmooth examples are presented to confirm theoretical result and superiority of the new scheme.
Anuradha Singh and J. P. Jaiswal
Hindawi Limited
The prime objective of this paper is to design a new family of optimal eighth-order iterative methods by accelerating the order of convergence of the existing seventh-order method without using more evaluations for finding simple root of nonlinear equations. Numerical comparisons have been carried out to demonstrate the efficiency and performance of the proposed method. Finally, we have compared new method with some existing eighth-order methods by basins of attraction and observed that the proposed scheme is more efficient.