TY - JOUR
T1 - A Family of High Order Numerical Methods for Solving Nonlinear Algebraic Equations with Simple and Multiple Roots
AU - Baccouch, Mahboub
N1 - Funding Information:
Acknowledgements I would like to thank the anonymous referees for their constructive comments and remarks which helped improve the quality and readability of the paper. This research was supported by the University Committee on Research and Creative Activity (UCRCA Proposal 2016-01-F) at the University of Nebraska at Omaha.
Publisher Copyright:
© 2017, Springer (India) Private Ltd.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - In this paper, we present, analyze, and test a family of high order iterative methods for finding simple and multiple roots of nonlinear algebraic equations of the form f(x) = 0. The proposed method can achieve convergence of order p, where p≥ 2 is a positive integer. The standard Newton–Raphson method (p= 2 ) and the Chebyshev’s method (p= 3 ) are both special cases of this family of methods. The pth order method requires evaluation of the function and its derivative up to order p- 1 at each step. Several numerical experiments are provided to validate the theoretical order of convergence for nonlinear functions with simple and multiple roots.
AB - In this paper, we present, analyze, and test a family of high order iterative methods for finding simple and multiple roots of nonlinear algebraic equations of the form f(x) = 0. The proposed method can achieve convergence of order p, where p≥ 2 is a positive integer. The standard Newton–Raphson method (p= 2 ) and the Chebyshev’s method (p= 3 ) are both special cases of this family of methods. The pth order method requires evaluation of the function and its derivative up to order p- 1 at each step. Several numerical experiments are provided to validate the theoretical order of convergence for nonlinear functions with simple and multiple roots.
KW - High order iterative methods
KW - Newton’s method
KW - Nonlinear equations
KW - Order of convergence
KW - Root-finding problem
KW - Simple and multiple roots
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U2 - 10.1007/s40819-017-0405-6
DO - 10.1007/s40819-017-0405-6
M3 - Article
AN - SCOPUS:85065162591
VL - 3
SP - 1119
EP - 1133
JO - International Journal of Applied and Computational Mathematics
JF - International Journal of Applied and Computational Mathematics
SN - 2349-5103
ER -