Some improvements of Jarratt’s method with sixth-order convergence. (English) Zbl 1122.65329

Chun, Changbum

Appl. Math. Comput. 190, No. 2, 1432-1437 (2007).

Summary: We present a one-parameter family of variants of Jarratt’s fourth-order method for solving nonlinear equations. It is shown that the order of convergence of each family member is improved from four to six even though it adds one evaluation of the function at the point iterated by Jarratt’s method per iteration. Several numerical examples are given to illustrate the performance of the presented methods.

MSC:

65H05

Numerical computation of solutions to single equations

Keywords:

Newton’s method; iterative methods; nonlinear equations; order of convergence; Jarratt’s fourth-order method; numerical examples

References:

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