Oriental Journal of Computer Science and Technology

Open Access Open Access  Restricted Access Subscription Access

Eighteenth Order Convergent Method for Solving Non-Linear Equations


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

In this paper, we suggest and discuss an iterative method for solving nonlinear equations of the type f(x)=0  having eighteenth order convergence. This new technique based on Newton’s method and extrapolated Newton’s method. This method is compared with the existing ones through some numerical examples to exhibit its superiority.

Keywords

Iterative Method, Nonlinear Equation, Newton’s Method, Convergence Analysis, Higher Order Convergence.
User
Notifications
Font Size

  • I.K. Argyros, S.K. Khattri, An improved semi local convergence analysis for the Chebyshev method, Journal of Applied Mathematics and computing, 42(1, 2) (2013), 509-528, doi: 10.1007/s12190-0130-647-3.

  • M.A. Hafiz, Solving nonlinear equations using steffensen-type methods with optimal order of convergence, Palestine Journal of Mathematics, 3(1) , 113-119, (2014).

  • M.A. Hafiz, A new combined bracketing method for solving nonlinear equations, Journal of Mathematical and Computational Science, 3,(1)(2013).

  • M.A. Hafiz, S.M.H. Al-Goria, Solving nonlinear equations using a new tenthand seventh- order methods free from second derivative, International Journal of Differential Equations and Applications, 12(3) (2013), 169-183,2013, doi: 10.12732/ ijdea.v12i3.1344.

  • S.K. Khattri, Torgrim Log, Constructing thirdorder derivative-free iterative methods, Int. J. Comput. Math., 88(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, 592-601, (2012).

  • 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, 432-437, (2013).

  • Khal ida Inayat Noor, Muhammad Aslam Noor, Shaher Momani, Modified Householder iterative methods for nonlinear equations”, Applied Mathematics and Computation,190, 1534-1539, (2007), 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, 93,(1), 85-94, 2014.

  • Vatti V.B.Kumar, Mylapalli M. S. Kumar, Katragadda A. Kumari,Extrapolated NewtonRaphson Method, Math. Educ. 43(1), 103-108 (2009).


Abstract Views: 348

PDF Views: 3




  • Eighteenth Order Convergent Method for Solving Non-Linear Equations

Abstract Views: 348  |  PDF Views: 3

Authors

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

Abstract


In this paper, we suggest and discuss an iterative method for solving nonlinear equations of the type f(x)=0  having eighteenth order convergence. This new technique based on Newton’s method and extrapolated Newton’s method. This method is compared with the existing ones through some numerical examples to exhibit its superiority.

Keywords


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

References





DOI: https://doi.org/10.13005/ojcst%2F10.01.19