TY - JOUR
T1 - A Family of High Order Numerical Methods for Solving Nonlinear Algebraic Equations with Simple and Multiple Roots
AU - Baccouch, Mahboub
N1 - 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
SN - 2349-5103
VL - 3
SP - 1119
EP - 1133
JO - International Journal of Applied and Computational Mathematics
JF - International Journal of Applied and Computational Mathematics
ER -