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A New Biparametric Family of Two‐Point Optimal Fourth‐Order Multiple‐Root Finders

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  • Young Ik Kim
  • Young Hee Geum

Abstract

We construct a biparametric family of fourth‐order iterative methods to compute multiple roots of nonlinear equations. This method is verified to be optimally convergent. Various nonlinear equations confirm our proposed method with order of convergence of four and show that the computed asymptotic error constant agrees with the theoretical one.

Suggested Citation

  • Young Ik Kim & Young Hee Geum, 2014. "A New Biparametric Family of Two‐Point Optimal Fourth‐Order Multiple‐Root Finders," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:737305
    DOI: 10.1155/2014/737305
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    References listed on IDEAS

    as
    1. Young Ik Kim & Young Hee Geum, 2013. "A Two-Parameter Family of Fourth-Order Iterative Methods with Optimal Convergence for Multiple Zeros," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, February.
    2. Young Ik Kim & Young Hee Geum, 2013. "A Two‐Parameter Family of Fourth‐Order Iterative Methods with Optimal Convergence for Multiple Zeros," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
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    Cited by:

    1. Young Ik Kim & Young Hee Geum, 2016. "A Triparametric Family of Optimal Fourth‐Order Multiple‐Root Finders and Their Dynamics," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).

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