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Revisit of Jarratt method for solving nonlinear equations

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Abstract

In this paper, some sixth-order modifications of Jarratt method for solving single variable nonlinear equations are proposed. Per iteration, they consist of two function and two first derivative evaluations. The convergence analyses of the presented iterative methods are provided theoretically and a comparison with other existing famous iterative methods of different orders is given. Numerical examples include some of the newest and the most efficient optimal eighth-order schemes, such as Petkovic (SIAM J Numer Anal 47:4402–4414, 2010), to put on show the accuracy of the novel methods. Finally, it is also observed that the convergence radii of our schemes are better than the convergence radii of the optimal eighth-order methods.

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References

  1. Chun, C.: A geometric construction of iterative formulas of order three. Appl. Math. Lett. 23, 512–516 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cordero, A., Hueso, J.L., Martinez, E., Torregrosa, J.R.: Efficient three-step iterative methods with sixth order convergence for nonlinear equations. Numer. Algor. 53, 485–495 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Grau-Sanchez, M., Gutierrez, J.M.: Zero-finders methods derived from Obreshkov’s techniques. Appl. Math. Comput. 215, 2992–3001 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gupta, D.K., Parhi, S.K.: An improved class of regula falsi methods of third order for solving nonlinear equations in R. J. Appl. Math. Comput. 33, 35–45 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kou, J., Li, Y., Wang, X.: A modification of Newton method with third-order convergence. Appl. Math. Comput. 181, 1106–1111 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kung, H.T., Traub, J.F.: Optimal order of one-point and multipoint iteration. J. Assoc. Comput. Math. 21, 634–651 (1974)

    MathSciNet  Google Scholar 

  7. Sharma, J.R., Sharma, R.: A new family of modified Ostrowski’s methods with accelerated eighth order convergence. Numer. Algor. 54, 445–458 (2010)

    Article  MATH  Google Scholar 

  8. Sharma, J.R., Guha, R.K.: A family of modified Ostrowski methods with accelerated sixth-order convergence. Appl. Math. Comput. 190, 111–115 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Soleymani, F., Sharifi, M.: On a cubically iterative scheme for solving nonlinear equations. Far East J. Appl. Math. 43, 137–143 (2010)

    MathSciNet  MATH  Google Scholar 

  10. Petkovic, M.S.: On a general class of multipoint root-finding methods of high computational efficiency. SIAM J. Numer. Anal. 47, 4402–4414 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang, H., Li, A.: A family of derivative-free methods for nonlinear equations. Rev. Mat. Complut. (2010). doi:10.1007/s13163-010-0044-5

  12. Wang, X., Kou, J., Li, Y.: A variant of Jarratt method with sixth-order convergence. Appl. Math. Comput. 204, 14–19 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wang, X., Gu, C., Kou, J.: Semilocal convergence of a multipoint fourth-order super-Halley method in Banach spaces. Numer. Algor. (2010). doi:10.1007/s11075-010-9401-1

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Authors and Affiliations

  1. Department of Mathematics, Young Researchers Club, Zahedan Branch, Islamic Azad University, Zahedan, Iran

    Fazlollah Soleymani

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  1. Fazlollah Soleymani
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Correspondence to Fazlollah Soleymani.

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Soleymani, F. Revisit of Jarratt method for solving nonlinear equations. Numer Algor 57, 377–388 (2011). https://doi.org/10.1007/s11075-010-9433-6

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  • DOI: https://doi.org/10.1007/s11075-010-9433-6

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