New third and fourth order nonlinear solvers for computing multiple roots

Janak Raj Sharma

doi:10.1016/j.amc.2011.04.063

New third and fourth order nonlinear solvers for computing multiple roots

2011-08-01

8

PRE

AI

DOI：10.1016/j.amc.2011.04.063

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We present a new third order method for finding multiple roots of nonlinear equations based on the scheme for simple roots developed by Kou et al. [J. Kou, Y. Li, X. Wang, A family of fourth-order methods for solving non-linear equations, Appl. Math. Comput. 188 (2007) 1031-1036]. Further investigation gives rise to new third and fourth order families of methods which do not require second derivative. The fourth order family has optimal order, since it requires three evaluations per step, namely one evaluation of function and two evaluations of first derivative. The efficacy is tested on a number of relevant numerical problems. Computational results ascertain that the present methods are competitive with other similar robust methods. (C) 2011 Elsevier Inc. All rights reserved.

Keyword:

Nonlinear equations

Newton's method

Rootfinding

Multiple roots

Order of convergence

Efficiency

New third and fourth order nonlinear solvers for computing multiple roots

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