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A variant of Jarratt method with sixth-order convergence. (English) Zbl 1168.65346

Authors’ abstract: “We present a variant of the Jarratt method for solving nonlinear equations. Per iteration the new method adds the evaluation of the function at another point in the procedure iterated by Jarratt method. As a consequence, the local order of convergence is improved from four for Jarratt method to six for the new method. A new multistep iteration scheme, based on the new method, is developed and numerical tests verifying the theory are also given.”

Finally, the new methods are extended to systems of nonlinear equations.


MSC:
65H05Single nonlinear equations (numerical methods)
65H10Systems of nonlinear equations (numerical methods)