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New high-order convergence iteration methods without employing derivatives for solving nonlinear equations

✍ Scribed by Xinyuan Wu; Dongsheng Fu

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
341 KB
Volume
41
Category
Article
ISSN
0898-1221

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✦ Synopsis

A family of new iteration methods without employing derivatives is proposed in this paper. We have proved that these new methods are quadratic convergence. Their efficiency is demonstrated by numerical experiments. The numerical experiments show that our algorithms are comparable to well-known methods of Newton and Steffensen. Furthermore, combining the new method with bisection method we construct another new high-order iteration method with nice asymptotic convergence properties of the diameters {(bn -a,0}.

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