A family of Steffensen type methods with seventh-order convergence
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In this paper, based on some known fourth-order Steffensen type methods, we present a family of three-step seventh-order Steffensen type iterative methods for solving nonlinear equations and nonlinear systems. For nonlinear systems, a development of the inverse first-order divided difference operator for multivariable function is applied to prove the order of convergence of the new methods. Numerical experiments with comparison to some existing methods are provided to support the underlying theory.
KeywordsSteffensen’s method Newton’s method Derivative free Seventh-order convergence Root-finding
Mathematics Subject Classfications (2010)65H05 65B99
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