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In this paper, we present a new two-point fourth-order Jarratt-type scheme based on Hansen-Patrick's family for solving nonlinear equations numerically. In terms of computational cost, each method of the proposed class requires only three functional evaluations (viz. one evaluation of function and two rst-order derivatives) per full step to achieve optimal fourth-order convergence.Moreover, the local convergence analysis of the proposed methods is also given using hypotheses only on the rst derivative and Lipschitz constants. Furthermore, the proposed scheme can also determine the complex zeros without having to start from a complex initial guess as would be necessary with other methods. Numerical examples and comparisons with some existing methods are included to conrm the theoretical results and high computational efficiency.

Nonlinear equations, Jarratt-type methods, Kung-Traub conjecture, Local Convergence