A NEW THREE- STEP DERIVATIVE FREE ITERATIVE METHOD AND ITS DYNAMICS

Syamsudhuha Syamsudhuha (University of Riau)
M Imran (University of Riau)
Ayunda Putri (University of Riau)
Leli Deswita (University of Riau)
Riski Amelia (University of Riau)

Journal of the Indonesian Mathematical Society
Vol. 30 No. 3 (2024): NOVEMBER

A new free derivative iterative method is presented in this article. The method is developed by combining Newton’s method and Euler’s method. Deriva- tives in this method are approximated by forward difference, hyperbola and divided difference. The order of convergence is proven analytically to be of sixth order. Numerical results exhibit that the new method is comparable to other methods. Basins of attraction are also provided to support the proposed method.