Anuradha Singh

@iiitn.ac.in

Assistant Professor.
Indian Institute of Information Technology Nagpur

Anuradha Singh


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https://researchid.co/anuradhasingh
8

Scopus Publications

46

Scholar Citations

4

Scholar h-index

2

Scholar i10-index

Scopus Publications

  • On a Three-Step Efficient Fourth-Order Method for Computing the Numerical Solution of System of Nonlinear Equations and Its Applications
    Anuradha Singh
    Proceedings of the National Academy of Sciences India Section A Physical Sciences, 2020
    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.
  • An efficient fifth-order iterative scheme for solving a system of nonlinear equations and PDE
    Anuradha Singh
    International Journal of Computing Science and Mathematics, 2020
    This article, introduces an efficient fifth-order iterative technique for solving systems of nonlinear equations. The order of convergence of the proposed method has been verified by the computational order of convergence. Some numerical examples are employed to show the superiority of the proposed iterative method. The computational efficiency index has also been illustrated and analysed. The application of proposed scheme for solving nonlinear PDE has also been discussed here.
  • An efficient iterative scheme for computing multiple roots of nonlinear equations
    Anuradha Singh
    Proceedings 7th International Conference on Communication Systems and Network Technologies Csnt 2017, 2018
    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.
  • An efficient fifth-order Steffensen-type method for solving systems of nonlinear equations
    Anuradha Singh
    International Journal of Computing Science and Mathematics, 2018
    In this paper, we present a three-step Steffensen-type iterative method of order five for solving systems of nonlinear equations. Various particular cases of the proposed method are considered. The general form of computational efficiency of the proposed scheme is compared to existing techniques. Numerical examples are given to show the performance of the proposed method with some existing schemes. We observed from the comparison of the new scheme with some known methods that the proposed scheme shows high efficiency index than others.
  • A class of optimal eighth-order Steffensen-type iterative methods for solving nonlinear equations and their basins of attraction
    Anuradha Singh, J. P. Jaiswal
    Applied Mathematics and Information Sciences, 2016
    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.
  • An Efficient Family of Optimal Fourth-Order Iterative Methods for Finding Multiple Roots of Nonlinear Equations
    Anuradha Singh, J. P. Jaiswal
    Proceedings of the National Academy of Sciences India Section A Physical Sciences, 2015
    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.
  • Improving R-order convergence of derivative free with memory method by two self-accelerator parameters
    Anuradha Singh, J. P. Jaiswal
    Springer Proceedings in Mathematics and Statistics, 2015
    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.
  • An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics
    Anuradha Singh, J. P. Jaiswal
    Journal of Mathematics, 2014
    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.

RECENT SCHOLAR PUBLICATIONS

  • On a Three-Step Efficient Fourth-Order Method for Computing the Numerical Solution of System of Nonlinear Equations and Its Applications
    A Singh
    Proceedings of the National Academy of Sciences, India Section A: Physical … , 2020
    2020
    Citations: 2
  • An efficient fifth-order iterative scheme for solving a system of nonlinear equations and PDE
    A Singh
    International Journal of Computing Science and Mathematics 11 (4), 316-326 , 2020
    2020
    Citations: 3
  • An efficient fifth-order Steffensen-type method for solving systems of nonlinear equations
    A Singh
    International Journal of Computing Science and Mathematics 9 (5), 501-514 , 2018
    2018
    Citations: 15
  • An efficient family of optimal fourth-order iterative methods for finding multiple roots of nonlinear equations
    A Singh, JP Jaiswal
    Proceedings of the National Academy of Sciences, India Section A: Physical … , 2015
    2015
    Citations: 8
  • Improving R -Order Convergence of Derivative Free with Memory Method by Two Self-accelerator Parameters
    A Singh, JP Jaiswal
    Mathematical Analysis and its Applications: Roorkee, India, December 2014 … , 2015
    2015
    Citations: 1
  • A class of optimal eighth-order Steffensen-type iterative methods for solving nonlinear equations and their basins of attraction
    A Singh, JP Jaiswal
    arXiv preprint arXiv:1404.3053 , 2014
    2014
    Citations: 6
  • An Efficient Family of Optimal Eighth‐Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics
    A Singh, JP Jaiswal
    Journal of Mathematics 2014 (1), 569719 , 2014
    2014
    Citations: 11

MOST CITED SCHOLAR PUBLICATIONS

  • An efficient fifth-order Steffensen-type method for solving systems of nonlinear equations
    A Singh
    International Journal of Computing Science and Mathematics 9 (5), 501-514 , 2018
    2018
    Citations: 15
  • An Efficient Family of Optimal Eighth‐Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics
    A Singh, JP Jaiswal
    Journal of Mathematics 2014 (1), 569719 , 2014
    2014
    Citations: 11
  • An efficient family of optimal fourth-order iterative methods for finding multiple roots of nonlinear equations
    A Singh, JP Jaiswal
    Proceedings of the National Academy of Sciences, India Section A: Physical … , 2015
    2015
    Citations: 8
  • A class of optimal eighth-order Steffensen-type iterative methods for solving nonlinear equations and their basins of attraction
    A Singh, JP Jaiswal
    arXiv preprint arXiv:1404.3053 , 2014
    2014
    Citations: 6
  • An efficient fifth-order iterative scheme for solving a system of nonlinear equations and PDE
    A Singh
    International Journal of Computing Science and Mathematics 11 (4), 316-326 , 2020
    2020
    Citations: 3
  • On a Three-Step Efficient Fourth-Order Method for Computing the Numerical Solution of System of Nonlinear Equations and Its Applications
    A Singh
    Proceedings of the National Academy of Sciences, India Section A: Physical … , 2020
    2020
    Citations: 2
  • Improving R -Order Convergence of Derivative Free with Memory Method by Two Self-accelerator Parameters
    A Singh, JP Jaiswal
    Mathematical Analysis and its Applications: Roorkee, India, December 2014 … , 2015
    2015
    Citations: 1