On an Inverse Free Steffensen-Type Method for the Approximation of Stiff Differential Equations.

In this article, an inverse free Steffensen-type method is introduced. The method is applied to approximate the systems of equations associated to implicit schemes approximating a stiff differential equation. The method has quadratic convergence without evaluating neither any derivative nor inverse operator. Finally, hypotheses ensuring the semilocal convergence and the R-order of convergence are presented. [ABSTRACT FROM AUTHOR]