A family of fourth-order Steffensen-type methods with the applications on solving nonlinear ODEs. (English) Zbl 1223.65034

A family of fourth-order Steffensen-type two-step root-finders are proposed. Results of theoretical analysis and numerical experiments demonstrate that this family only uses three evaluations of the function per iteration to achieve the optimal fourth-order convergence for solving simple roots of nonlinear functions. The family also presents the opportunity to pursue iterative methods with better convergence than those of the typical second-order and third-order methods.


65H05 Numerical computation of solutions to single equations
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