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

Authors:
Xiaowu Li;Chunlai Mu;Jinwen Ma;Linke Hou
Affiliations:
College of Mathematics and Statistics, Chongqing University, Chongqing, People's Republic of China 400044;College of Mathematics and Statistics, Chongqing University, Chongqing, People's Republic of China 400044;School of Mathematical Sciences and LMAM, Peking University, Beijing, People's Republic of China 100871;Center for Chinese Agricultural Policy, Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, People's Republic of China 100101
Venue:
Numerical Algorithms
Year:
2011

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Abstract

This paper presents a fifth-order iterative method as a new modification of Newton's method for finding multiple roots of nonlinear equations with unknown multiplicity m. Its convergence order is analyzed and proved. Moreover, several numerical examples demonstrate that the proposed iterative method is superior to the existing methods.