Article

Two step optimal Jarratt-type fourth order methods using two weight functions for solving nonlinear equations

Abstract

In this paper, we have presented many classes of two step optimal Jarratt-type fourth order methods using two weight functions. In terms of computational point of view (we suppose all functions and derivative evaluations have the same computational cost), our methods require three evaluations (one function and two first derivatives) and have convergence order four. Hence, these methods have high efficiency index 1.5874 and are optimal in the sense of Kung-Traub conjecture. Some known results can be regarded as particular cases. Some numerical examples are tested to know the performance of the methods which verifies the theoretical results.