Optimal Order of One-Point and Multipoint Iteration
Journal of the ACM (JACM)
New eighth-order iterative methods for solving nonlinear equations
Journal of Computational and Applied Mathematics
Accurate fourteenth-order methods for solving nonlinear equations
Numerical Algorithms
Finding the solution of nonlinear equations by a class of optimal methods
Computers & Mathematics with Applications
Optimal eighth-order simple root-finders free from derivative
WSEAS Transactions on Information Science and Applications
An efficient twelfth-order iterative method for finding all the solutions of nonlinear equations
Journal of Computational Methods in Sciences and Engineering
Hi-index | 0.09 |
This paper proposes two classes of three-step without memory iterations based on the well known second-order method of Steffensen. Per computing step, the methods from the developed classes reach the order of convergence eight using only four evaluations, while they are totally free from derivative evaluation. Hence, they agree with the optimality conjecture of Kung-Traub for providing multi-point iterations without memory. As things develop, numerical examples are employed to support the underlying theory developed for the contributed classes of optimal Steffensen-type eighth-order methods.