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Two new classes of optimal Jarratt-type fourth-order methods. (English) Zbl 1239.65030
Summary: We investigate the construction of some two-step without memory iterative classes of methods for finding simple roots of nonlinear scalar equations. The classes are built through the approach of weight functions and these obtained classes reach the optimal order four using one function and two first derivative evaluations per full cycle. This shows that our classes can be considered as Jarratt-type schemes. The accuracy of the classes is tested on a number of numerical examples. And eventually, it is observed that our contributions take less number of iterations than the compared existing methods of the same type to find more accurate approximate solutions of the nonlinear equations.
MSC:
65H05Single nonlinear equations (numerical methods)
References:
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