Newton type iterative methods with higher order of convergence

Authors

  • Pankaj Jain South Asian University, India
  • Chet Raj Bhatta Tribhuvan University, Nepal
  • Jivandhar Jnawali Tribhuvan University, Nepal

DOI:

https://doi.org/10.33993/jnaat451-1049

Keywords:

Newton method, Secant method, Iterative method, Nonlinear equation, Order of convergence
Abstract views: 389

Abstract

Newton type iterative methods are obtained with higher order of convergence and with higher efficiency. The methods have been compared with the similar existing methods of recent times.

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References

B. Bradie, A Friendly Introduction to Numerical Analysis, Pearson, 2007.

D. Jain, Families of Newton-like methods with fourth-order convergence, Int. J. Comp. Math., 90 (2013), pp. 1072–1082, http://dx.doi.org/10.1080/00207160.2012.746677 DOI: https://doi.org/10.1080/00207160.2012.746677

D. Jain, Newton and Steffensen type methods with flexible order of convergence, Jordanian J. Math. Stat.,8 (2015), pp. 43-57.

D. Jain and B. Gupta, Two step Newton and Steffensen type methods for solving nonlinear equations, Tbiliai Math. J.,5 (2012), pp. 17-29. DOI: https://doi.org/10.32513/tbilisi/1528768886

P. Jain, Steffensen type methods for solving non-linear equations, Appl. Math. Comput., 194 (2007), pp. 527-533, http://dx.doi.org/10.1016/j.amc.2007.04.087 DOI: https://doi.org/10.1016/j.amc.2007.04.087

A.B. Kasturiarachi, Leap frogging Newton’s method, Int. J. Math. Educ. Sci. Technol., 33 (2002), pp. 521-527, http://dx.doi.org/10.1080/00207390210131786 DOI: https://doi.org/10.1080/00207390210131786

T. J. McDougall and S. J. Wotherspoon, A simple modification of Newton’s method to achieve convergence of order 1+√2, Appl. Math. Lett., 29 (2014), pp. 20-25, http://dx.doi.org/10.1016/j.aml.2013.10.008 DOI: https://doi.org/10.1016/j.aml.2013.10.008

S. Weerakoon and T.G.I. Fernando, A variant of Newton’s method with accelerated third-order convergence, Appl. Math. Lett., 13 (2002), pp. 87-93, http://dx.doi.org/10.1016/S0893-9659(00)00100-2 DOI: https://doi.org/10.1016/S0893-9659(00)00100-2

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Published

2016-04-22

How to Cite

Jain, P., Bhatta, C. R., & Jnawali, J. (2016). Newton type iterative methods with higher order of convergence. J. Numer. Anal. Approx. Theory, 45(1), 14–26. https://doi.org/10.33993/jnaat451-1049

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