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Fourth-Order Derivative-Free Optimal Families of King’s and Ostrowski’s Methods

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Mathematical Analysis and its Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 143))

Abstract

In this paper, we present several new fourth-order optimal schemes that do not require any derivative evaluation for solving nonlinear equations, numerically. The presented approach of deriving these families is based on approximating derivatives by finite difference and weight function approach. The fourth-order derivative-free optimal families of King’s and Ostrowski’s methods are the main findings of the present work. Further, we have also shown that the families of fourth-order methods proposed by Petković et al., Appl Math Comput 217:1887–1895 (2010) [12] and Kung-Traub, J ACM 21:643–651 (1974) [8] are special cases of our proposed schemes. The proposed methods are compared with their closest competitors in a series of numerical experiments. All the methods considered here are found to be more effective to similar robust methods available in the literature.

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References

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Acknowledgments

The authors wish to thank the anonymous referees for their valuable suggestions and comments.

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg, 3209, South Africa

    Ramandeep Behl & S. S. Motsa

  2. University Institute of Engineering and Technology, Panjab University, Chandigarh, 160 014, India

    Munish Kansal & V. Kanwar

Authors
  1. Ramandeep Behl
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  2. S. S. Motsa
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  3. Munish Kansal
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  4. V. Kanwar
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Corresponding author

Correspondence to Ramandeep Behl .

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Editors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    P. N. Agrawal

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    R. N. Mohapatra

  3. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Uaday Singh

  4. Dept. of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

    H. M. Srivastava

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Behl, R., Motsa, S.S., Kansal, M., Kanwar, V. (2015). Fourth-Order Derivative-Free Optimal Families of King’s and Ostrowski’s Methods. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_29

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