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A New Second-Order Iteration Method for Solving Nonlinear Equations

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  • Shin Min Kang
  • Arif Rafiq
  • Young Chel Kwun

Abstract

We establish a new second-order iteration method for solving nonlinear equations. The efficiency index of the method is 1.4142 which is the same as the Newton-Raphson method. By using some examples, the efficiency of the method is also discussed. It is worth to note that (i) our method is performing very well in comparison to the fixed point method and the method discussed in Babolian and Biazar (2002) and (ii) our method is so simple to apply in comparison to the method discussed in Babolian and Biazar (2002) and involves only first-order derivative but showing second-order convergence and this is not the case in Babolian and Biazar (2002), where the method requires the computations of higher-order derivatives of the nonlinear operator involved in the functional equation.

Suggested Citation

  • Shin Min Kang & Arif Rafiq & Young Chel Kwun, 2013. "A New Second-Order Iteration Method for Solving Nonlinear Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-4, April.
    • Handle: RePEc:hin:jnlaaa:487062
    DOI: 10.1155/2013/487062
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    Cited by:

    1. Christian Vanhille, 2020. "An Improved Secant Algorithm of Variable Order to Solve Nonlinear Equations Based on the Disassociation of Numerical Approximations and Iterative Progression," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(6), pages 1-50, December.

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