Abstract
The principal objective of this work is to propose a fourth order scheme for solving a nonlinear equation. In terms of computational cost, per iteration, the fourth order method uses two evaluation of the function and one evaluation of first derivative. So the method has satisfied the Kung-Traub optimality conjecture. In addition, the theoretical convergence properties of our schemes are fully explored with the help of the main theorem that demonstrates the convergence order. The performance and effectiveness of our optimal iteration functions have compared with the existing competitors on some standard academic problems.
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