A Family of Fifth-Order Iterative Methods for Finding Multiple Roots of Nonlinear Equations

2021 ◽  
Vol 14 (2) ◽  
pp. 186-199
Author(s):  
J. R. Sharma ◽  
H. Arora
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Multiple Roots ◽  
Fifth Order

scholarly journals Three New Optimal Fourth-Order Iterative Methods to Solve Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Gustavo Fernández-Torres ◽  
Juan Vásquez-Aquino
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
Classical Method ◽  
Multiple Roots ◽  
Order Convergence ◽  
Numerical Examples ◽  
Optimal Methods

We present new modifications to Newton's method for solving nonlinear equations. The analysis of convergence shows that these methods have fourth-order convergence. Each of the three methods uses three functional evaluations. Thus, according to Kung-Traub's conjecture, these are optimal methods. With the previous ideas, we extend the analysis to functions with multiple roots. Several numerical examples are given to illustrate that the presented methods have better performance compared with Newton's classical method and other methods of fourth-order convergence recently published.

scholarly journals Optimal iterative methods for finding multiple roots of nonlinear equations using free parameters

2017 ◽  
Vol 56 (7) ◽  
pp. 1884-1901 ◽  
Author(s):  
Fiza Zafar ◽  
Alicia Cordero ◽  
R. Quratulain ◽  
Juan R. Torregrosa
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Multiple Roots ◽  
Free Parameters

scholarly journals A Two-Parameter Family of Fourth-Order Iterative Methods with Optimal Convergence for Multiple Zeros

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Young Ik Kim ◽  
Young Hee Geum
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Numerical Experiments ◽  
Harmonic Mean ◽  
Optimal Order ◽  
Multiple Roots ◽  
Multiple Zeros ◽  
Asymptotic Error ◽  
Two Parameter

We develop a family of fourth-order iterative methods using the weighted harmonic mean of two derivative functions to compute approximate multiple roots of nonlinear equations. They are proved to be optimally convergent in the sense of Kung-Traub’s optimal order. Numerical experiments for various test equations confirm well the validity of convergence and asymptotic error constants for the developed methods.

scholarly journals A New Biparametric Family of Two-Point Optimal Fourth-Order Multiple-Root Finders

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Young Ik Kim ◽  
Young Hee Geum
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Multiple Root ◽  
Multiple Roots ◽  
Asymptotic Error ◽  
Error Constant ◽  
Asymptotic Error Constant

We construct a biparametric family of fourth-order iterative methods to compute multiple roots of nonlinear equations. This method is verified to be optimally convergent. Various nonlinear equations confirm our proposed method with order of convergence of four and show that the computed asymptotic error constant agrees with the theoretical one.

scholarly journals New Fourth and Fifth-Order Iterative Methods for Solving Nonlinear Equations

2015 ◽  
Vol 06 (08) ◽  
pp. 1220-1227
Author(s):  
Muhammad Saqib ◽  
Muhammad Iqbal ◽  
Shahid Ali ◽  
Tariq Ismaeel
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fifth Order

Fifth-order iterative methods for solving nonlinear equations

2007 ◽  
Vol 188 (1) ◽  
pp. 406-410 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fifth Order

Fifth-order iterative method for finding multiple roots of nonlinear equations

2010 ◽  
Vol 57 (3) ◽  
pp. 389-398 ◽  
Author(s):  
Xiaowu Li ◽  
Chunlai Mu ◽  
Jinwen Ma ◽  
Linke Hou
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Multiple Roots ◽  
Fifth Order
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