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Second Derivative Free Eighteenth Order Convergent Method for Solving Non-Linear Equations


Affiliations
1 Dept. of Engineering Mathematics, Andhra University, Visakhapatnam, India
2 Dept. of Mathematics, Gitam University, Visakhapatnam, India
 

In this paper, the Eighteenth Order Convergent Method (EOCM) developed by Vatti et.al is considered and this method is further studied without the presence of second derivative. It is shown that this method has same efficiency index as that of EOCM. Several numerical examples are given to illustrate the efficiency and performance of the new method. AMS Subject Classification: 41A25, 65K05, 65H05.

Keywords

Iterative Method, Nonlinear Equation, Newton’s Method, Convergence Analysis, Higher Order Convergence.
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  • M.A. Hafiz, Solving nonlinear equations using steffensen-type methods with optimal order of convergence, Palestine Journal of Mathematics, 3, No: 1 (2014), 113-119.

  • M.A. Hafiz, A new combined bracketing method for solving nonlinear equations, Journal of Mathematical and Computational Science, 3, No.1 (2013)..

  • M.A. Hafiz, S.M.H. Al-Goria, Solving nonlinear equations using a new tenth-and seventhorder methods free from second derivative, International Journal of Differential Equations and Applications, 12, No. 3 (2013), 169183,2013, doi: 10.12732/ijdea.v12i3.1344.

  • S.K. Khattri, Torgrim Log, Constructing thirdorder derivative-free iterative methods, Int. J. Comput. Math., 88, No. 7 (2011), 1509-1518, doi: 10.1080/00207160.2010520705.

  • S.K. Khattri, Quadrature based optimal iterative methods with applications in high precision computing, Numer. Math. Theor. Meth. Appl., 5 (2012), 592-601.

  • S.K. Khattri, Trond Steihaug, Algorithm for forming derivative-free optimal methods, , Numerical Algorithms, (2013), doi: 10.1007/ s11075-013-9715-x.

  • Mohamed S.M. Bahgat, M.A. Hafiz, New two-step predictor-corrector method with ninth order convergence for solving nonlinear equations, Journal of Advances in Mathematics , 2 (2013), 432-437.

  • Khalida Inayat Noor, Muhammad Aslam Noor, Shaher Momani, Modified Householder iterative methods for nonlinear equations”, Applied Mathematics and Computation, 190 (2007), 1534-1539, doi: 10.1016/j.

  • amc.2007.02.036.

  • Mohamed S.M. Bahgat, M.A. Hafiz, Threestep iterative method with eighteenth order convergence for solving nonlinear equations, Int. Journal of Pure and Applied Mathematics, Vol. 93, No. 1, 2014, 85-94.

  • Vatti V.B.Kumar, Mylapalli M. S. Kumar, Katragadda A. Kumari,Extrapolated NewtonRaphson Method, Math. Educ. 43, No. 1, 103-108 (2009).

  • Vatti V. B. K, Sri R, Mylapalli M. S. K., Eighteenth Order Convergent Method for Solving Non-Linear Equations. Orient.J. Comp. Sci. and Technol;10(1), 144-150 (2017).

  • Vatti V. B. K, Ramadevi Sri, Mylapalli M. S. K., Two Step Extrapolated Newton’s Method with High Efficiency Index, Journal of Advanced Research in Dynamical and Control Systems; 9(5), 08-15 (2017).


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  • Second Derivative Free Eighteenth Order Convergent Method for Solving Non-Linear Equations

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Authors

V. B. Kumar Vatti
Dept. of Engineering Mathematics, Andhra University, Visakhapatnam, India
Ramadevi Sri
Dept. of Engineering Mathematics, Andhra University, Visakhapatnam, India
M. S. Kumar Mylapalli
Dept. of Mathematics, Gitam University, Visakhapatnam, India

Abstract


In this paper, the Eighteenth Order Convergent Method (EOCM) developed by Vatti et.al is considered and this method is further studied without the presence of second derivative. It is shown that this method has same efficiency index as that of EOCM. Several numerical examples are given to illustrate the efficiency and performance of the new method. AMS Subject Classification: 41A25, 65K05, 65H05.

Keywords


Iterative Method, Nonlinear Equation, Newton’s Method, Convergence Analysis, Higher Order Convergence.

References





DOI: https://doi.org/10.13005/ojcst%2F10.04.19